The Mishna Brura (Beiur Halachah 239:1, s.v. samuch) questions whether one should say it if he thinks he will not fall asleep before Alos HaShachar, even if it is currently before Alos HaShachar, and says that it should definitely not be said after Alos HaShachar.
The Shaari Teshuva O.C. 239:1 s.v. 2 mentions opinions based on Kabbalistic reasons that one ...
Sefer Seder Hayom from Rabbi Moshe Ben Machir.First edition (Venezzia) in year שנ"ט" (1599)". See here
At the begining of the Sefer:
ובקומו מיד מודה אני מלפניך מלך חי וקים שהחזרת בי נשמתי בחמלה רבה אמונתך. ואין צריך לזה נטילת ידיים כי אפילו יהיו דיו מטונפות אין חשש כיון שאינו מזכיר לא שם ולא כינוי.
When he wake up right away "mode ani.....
In short: there isn't, or at least, not sufficient evidence.
The author of the article quoted in the question seems to misunderstand the sources he quotes. While it may be true that the Rashbam interpreted verse in question (Genesis 1:5) in a way that implies that night follows the day, he is in no way making a legal statement, and as he himself says ...
According to R' Rabbi Moishe Dovid Lebovits
According to the basic reading of the Shulchan Aruch it seems that one should wash for bread every morning in order to have pas shacharis.(59) However, many say one is not required to eat bread, and whatever one eats in the morning is sufficient, as long as it is filling.(60) Some say one should be careful to have ...
This appears to be a variant1 of "קדרותא דצפרא" (the blackness of morning), which is an expression found in the Zohar (e.g. Vayishlach 170a, English translation by Prof. Daniel Matt).
The idea you mention is expressed by the Zohar there (per emended2 translation linked above):
Everyone asks, Who is this looking forth like the dawn? - at first the ...
Perhaps you mean the Zohar on Numbers Volume 3 249a-b (הזהר לספר במדבר ח״ג דף רמט ע״ב) where he connects the phrase קדרותא דצפרא to the break of dawn (אילת השחר). The other 2 places he uses the phrase קדרותא דצפרא are on Genesis Vol 1 40b and 170a.
In one wakes up after Chatzot HaLayla he should pray Arvit and after Arvit, bless Birkot HaShachar, and even if he goes back to sleep after all of that he does not bless Birkot HaShachar again in the morning.
There is a debate regarding "הנותן לשכוי בינה" which the Shulchan Aruch (46, 13) says not to bless before Alois HaShachar but the Mishna Berura brings ...
In the קיצור ש''ע ילקוט יוסף it says in סימן רלט - דין קריאת שמע שעל המטה:
One only says Hamapil with its ending Bracha until midnight.
After midnight one need not say Hamapil, but it's a good idea to say it without the final Bracha.
One who goes to sleep towards morning and will only fall asleep after Amud Hashachar need not say Hamapil.
א: ברכת ''...
Prayers in the siddur that can be said before dawn:
From Tefila Kehilchata
3 (8) If you get up after (halachic) midnight, you can say the morning blessings, except (1) “Elokai Neshomo ..” (2) “Hamaavir sheina” which can be said without Shem and Malchus and (3) “Hanosain Lasechvi” which should only be said after dawn. (O Ch 47 (13) MB )
3 (11) ...
Being that I am not able to comment on other posts yet, I have to do it this way.
I once heard in the name of a well-respected Rosh Yeshiva in Eretz Yisroel that pas shacharis is whatever you need to eat in the morning, not specifically bread or bread products.
According to that, Trix could be pas shacharis.