It's an excellent question Sarah and one that requires careful consideration and thoughtful reflection.
First, please bear in mind that the subjects mentioned in the 'answer' you found are borrowing heavily from the Prophets, midrashic and kabbalistic sources. So many of the ideas presented are to be understood allegorically, meaning interpretively, according to traditions passed down from generation to generation.
It is also appropriate to point out that your question is both timely and relevant from the perspective that we are living in great anticipation of the complete and final redemption spoken of throughout the Torah. And as we are reminded in the Aleinu prayer, during that time, all the inhabitants of the earth will come to serve the Creator together, like is discussed in the censored section of the Mishnah Torah, Laws of Kings and Their Wars, chapter 11 at the end.
But, the plans of the creator of the world--no person can understand them for our ways are not the same as His ways and our plans are not His plans. And all of these things about Jesus of Nazareth, and about that Ishmaelite who rose after him--they are only to make the path for the King Messiah straight, and to fix the whole world for worshipping G-d together, as it is said, "For I will give the peoples clear speech, for them all to call out the name of G-d, and to worship Him with one purpose (Zephaniah 3:9)
How? The whole world is already filled with the words of the Messiah, and the words of the Torah, and the words of the Mitzvot, and these words have been spread on distant islands, and to many peoples of uncircumcised hearts, and they deal with these words, and with the mitzvot of the Torah--they say 'These mitzvot were true but they are already nullified in this time, they aren't applicable forever.' And they say, 'There are things hidden in them, and they're not just a simple meaning, and the Messiah already came and revealed their secrets.'
And when the King Messiah rises for real, and he succeeds, and he is lifted up and exalted, they will immediately return and will know that their ancestors passed down lies to them and that their prophets and their ancestors made them do wrong.
The essential difference between the Jewish and Christian view of 'original sin' is about the source of sin.
The Christian concept is that 'sin' originates through a second 'power', which they refer to as the devil or Satan. The Christian view is that this 'power' is in a state of rebellion against G-d. It implies that there are two 'G-ds'. G-d created things in a state of perfection and without blemish. There is no sin and no death. And this was, according to Christian teaching, what G-d desired. Satan rebelled and challenged G-d and claimed dominion for himself. And this evolved into Satan influencing the serpent, who in turn influenced the first woman, who in turn caused sin to come into the world and then caused all other created things to sin and this caused death. And like you find in the fifth chapter of Romans which you cite, all of creation can only be saved from this terrible consequence by accepting Jesus as your personal intermediary between you and G-d.
But such an idea is contrary to Jewish teaching and is a denial of G-d's unity like is taught in Mishnah Torah, Sefer Maddah, Chapter 1:1 and 1:5-6.
The foundation of foundations and pillar of wisdoms is to know that there is a Primary Cause and He causes to exist all that exists. And everything that exists from Heaven to Earth and everything in between would not exist except from the truth of His existence.
G-d is one. He is not two and not more than two. Rather, He is one and His unity is unlike the unity of anything else that exists in the world. He is not like one genus that includes many individuals. And He is not like one body that can be divided into parts and extremities. Rather, His unity is such that there is no unity like His in the world. If there were many gods, they would possess bodies and forms, because things which are counted as equal in their existences are not separate one from the other, except in regard to the events that happen to bodies and forms. And if the Creator had a body and a form, He would have a time period and an end, because it is impossible to be a body that does not have a time period. And everything which possesses a time period and an end, also possesses an time period and limit to its power. And our G-d, blessed be His name, since His strength has no end and nothing to disrupt it - since the sphere revolves continuously (forever) - His strength is not the strength of a body. And since He does not have a body, events do not occur to Him as they occur to bodies, which can be split and divided by something else. Therefore it is impossible that He be anything but one. And the knowledge of this matter is a positive commandment, as it says, "The L-rd is our G-d, the L-rd is One" (Deut. 6:4).
And so the question still remains, 'What is the source of sin according to Jewish tradition and the Torah?'
This is discussed, among other places in Bereshit Rabbah which explains that the final events of the six days of creation, meaning the creation of Adam HaRishon, his division into two (Adam and Chava) and the subsequent 'dressing in skins', meaning becoming dressed in physicality, were actually the ultimate expression of the paradigm which G-d had intended from the very beginning of creation and even before creation. It follows the same model as the single light of the first day and that light being divided into two great lights, followed by one of those lights being reduced in stature.
And this paradigm follows what is discussed in kabbalistic literature about the light or expression of G-d creating the 'Makom Panoy' (empty place) and then bringing about the reintroduction of that first light via the 'Kav' and its interaction with the 'Reshimah' or 'residue' inside the Makom Panoy. And this paradigm also is the model of conception, gestation and birth.
And this infinitely repeating system is what is transmitted through the Torah. The same Torah which is described as 'G-d's will' and which G-d 'looked into' two thousand years before the creation. The same Torah which said 'Adam sinned' two thousand years before the creation, meaning before the creation of Adam HaRishon.
In other words, the source of sin is also from the Creator of everything and ultimately serves and expresses His will.
The reference from the Ari z"l, which is from the opening chapters of Sha'ar HaGilgulim, is only expressing the unity and common purpose of all mankind which is to serve the 'Owner of all' (Koneh HaKol) like is said in the opening blessings of the Amidah prayer.
And so this brings us to try to better understand the words of Rav Ami quoted above that, "אין מיתה בלא חטא". This is commonly translated as, 'there is no death without sin.' But the word 'חטא' has several different meanings aside from 'sin' or 'error' or 'mistake' which help to give understanding to this teaching. 'חטא' also has a meaning of cleansing like is found in Mishnah Yoma 5:5 and also the Talmud on the same subject, Yoma 58b and similarly Chullin 27a. 'חטא' also has a meaning of 'to cause someone to be generous or lenient' like is found in Kohelet Rabba on 9:18.
So this suggests that the process of introducing 'death' to the world is in order to have a process of cleansing and to cause G-d to reveal His quality of generosity and leniency. This is the concept of 'teshuvah' and G-d's 13 aspects of mercy.
And this leads to the final discussion in the answer that you cited. Namely, the Aggadic expression from the Sages, "תנו רבנן ארבעה מתו בעטיו של נחש".
This translates as 'The Rabbis learned that four died as a result of the fangs of the serpent' (The 'serpent' mentioned here is the 'Nachash'.)
To which the person writing that answer then brought Rahsi's comment on this statement:
בעטיו של נחש - בעצתו של נחש כלומר לא היו ראוין למות אלא שנגזרה גזירת מיתה על כל תולדותיו של אדם הראשון בעצתו של נחש בעטיו תרגום של עצתו כדכתיב (דניאל ו) אתייעטו כל וגו' וכן התיב עטא וטעם (שם ב):
'Through the fangs of the serpent' - Through the advice of the serpent. That is to say that they were not deserving of death except through the decree of death on all the descendants of Adam HaRishon. 'Through the advice of the serpent', the word for advice 'בעצתו' in Aramaic is 'בעטיו' (which translates in Hebrew as 'its fangs'), like is written in Daniel 6:8 and 2:14.
So Rashi is explaining this Aggadic teaching according to the plain grammatical meaning. But that raises the additional question of what exactly is this 'serpent' (נחש). Serpents have fangs, but they do not give advice.
And so, if we accept what Rashi points out, that the Rabbis were pointing to an unusual 'inner teaching' through this expression that is associated with the book of Daniel, we need to ask what is the nature of this teaching. How does the letter 'ט' in the word 'בעטיו' become the letter 'צ' of the word 'בעצתו'?
This happens through the kabbalistic permutation taught to the Prophets called 'Ick-Bachar' (אי״ק-בכ״ר). The letters of the alphabet are divided into ones, tens and hundreds. They are interchangeable and imply specific concepts and spiritual transformations when they are exchanged.
So for example, the 'Aleph' can be exchanged for the 'Yud' or the 'Kof' and the 'Beit' can be exchanged for the 'Kaf' or the 'Reish', and so on. In the case of the letter 'Tet', it is interchangeable with the letters 'Tzadik' and final 'Tzadik'.
And if this is the nature of the teaching being discussed, then it would be relevant to apply similar kabbalistic transformations to the idea of the 'serpent' (נחש) in order to understand exactly who this is giving 'advice'.
The letter 'Nun' in Nachash (נחש) is equal to the sum of the letters 'Mem' and 'Yud' (מ״י).
And this suggests that the 'Nachash' giving this advice here can also be understood to mean 'Moshiach' (מישח). That the one who ultimately is destined to be responsible for completing this whole process, the entire purpose of creation, the concealing of G-d's light, the introduction of death and bringing the entire world to return to G-d through teshuvah and eternal life, is the one who gives the advice, namely our righteous Moshiach.
So the Jewish view is that what you are calling 'original sin', something absolutely negative according to the Christian view, is actually part of G-d's plan and is according to His will. It is positive and will result in the bestowing of His blessings of true good upon all of creation.