I think you made a calculation error here, because when I add them up I get 603,550 as the passuk says. Note that 40,500 is exactly the number of people in Shevet Ephraim; did you forget to count them in tallying up these numbers?
603,550 excludes the Levites:
Altogether this equals 603,550, as it says in Bamidbar (1:46). And as the very next passuk (1:47) says:
וְהַלְוִיִּ֖ם לְמַטֵּ֣ה ...
Coincidentally, just today I saw an explanation for this issue in Dr. Yitzchak Meitlis's book Parashat Derachim. He explains that there are four differences between the two censuses:
In the second census, there was no order to count specifically the males like in the first census.
No women are mentioned in the first census, while in the second one the ...
By the Meraglim, the decree was that "in this desert, your carcasses will fall, for all of your countings and all of your numbers, from the age of 20 and older..." (Bamidbar 14:29).
The Gemara (Bava Basra 121b) derives by a gezeirah shavah - the common usage of "and older" here and by Erchin (Vayikra 27:7) - that the decree was for 20 to 60. As this was ...
The easy answer is provided by Bamidbar 1:47-9, the Levites were excluded from the Tribal Count.
וְהַלְוִיִּ֖ם לְמַטֵּ֣ה אֲבֹתָ֑ם לֹ֥א הָתְפָּקְד֖וּ בְּתוֹכָֽם׃
The Levites, however, were not recorded among them by their ancestral tribe.
וַיְדַבֵּ֥ר יְהוָ֖ה אֶל־מֹשֶׁ֥ה לֵּאמֹֽר׃
For the LORD had spoken to Moses, saying:
אַ֣ךְ אֶת־מַטֵּ֤ה לֵוִי֙ לֹ֣א ...
Rashi to Exodus 30:12 explains that counting Jews directly incites the Evil Eye, which, in turn, causes a plague.
ולא יהיה בהם נגף. שֶׁהַמִּנְיָן שׁוֹלֵט בּוֹ עַיִן הָרָע, וְהַדֶּבֶר בָּא עֲלֵיהֶם, כְּמוֹ שֶׁמָּצִינוּ בִימֵי דָּוִד (שמואל ב כ"ד):
”That there not be calamity among them” - for the Evil Eye rules through counting, and a plague comes upon ...
Your question poses 3 verses that seem to indicate that Israel was a smaller nation. Regarding the first 2 verses, see Rashbam that answers both of them
He says that both verses are connected. That all 7 nations together were larger than the Israelites. Then it goes on to state ...
Those who were regarded as able to actively serve in the public domain were being counted. Those over sixty were in effect retired from the army. Thus when the punishment of the 40 years was decreed, those who would have served in the army (20 to 60) at that time were being punished. Those below the age of 20 would not have been eligible to be drafted.
I always peek at the Targumim and indeed, Yonoson translates the first verse as:
"לָא מִן בִּגְלַל דְּאַתּוּן גֵּיוְתָנִין מִן כֻּלְהוֹן אוּמַיָא צָבֵי יְיָ בְּכוֹן וְאִתְרְעֵי בְּכוֹן אֱלָהֵן דְּאַתּוּן מַכִּיכֵי רוּחָא וְעִנְוְותָנִין מִכָּל עַמְמַיָא", meaning "you are the most humble and meek of all nations".
That means that he was ...
When my son was very little, he commented on this verse to me: Israel must have been in the desert for a really long time, if they didn't know if they were the biggest nation or the smallest nation!
I don't think the Torah was being "sarcastic", ח"ו. Israel's numbers were actually great; Moses said they were "like the stars in heaven for ...
The problem was not the census itself, but that David counted the people directly, instead of using something else to count them (Saul used shards of pottery to count the people. Each one gave a shard and then he counted the shards).
See Yuma 22B.
Read all about it here, and some reasons given here.
Possibly it's an issue of hora'as sha'ah. See ... all of maseches Horayos for detailed discussion on how Beis Din handles broadcasting improper halachic rulings that cause the public to commit an aveirah.
"Ein sheliach" works potentially in two different ways - 1) divrei harav vidivrei hatalmid, and 2) Chazal not giving the capacity for shlichus in the case ...