The commentator Rashi explains that the reference is not to numbers, but to estimation:
you regard yourselves as small, as, e.g., Abraham did who said, (Genesis 18:27) “For I am dust and ashes", and as, e.g., Moses and Aaron did who said, (Exodus 16:7) “And we, what are we?".
I do not believe the Torah is putting forth a proof of its own truth. The passuk is telling us that we should consider these acts of God, which have not been claimed anywhere else, as a demonstration of God's greatness over all other forces. The miracles are assumed to be true, and we need a refresher of how to view them and appreciate what it means.
As a ...
You can read in detail about the issue in this great article. To keep it short, Shevuot 20b mentions that the two versions were said in a single utterance, which is beyond human comprehension:
כדתניא זכור ושמור בדיבור אחד נאמרו, מה שאין יכול הפה לדבר, ומה שאין האוזן יכול לשמוע.
As it has been taught: Remember and keep were pronounced in a single ...
Rashi to Tehillim 36:3 seems to write the way you understand it (ie Hashem causes the rasha to slip/err):
כי החליק. הפשע על הרשע בחלקלקות בעיניו כדי שימצא הקב"ה את עונו לשנוא אותו:
Hashem has the wicked one sin through the smoothing over the transgression in [the rasha's] eyes in order that Hashem finds his sin to hate
Here's an explanation you might find satisfactory:
The first difference between the 2 versions is who said it - the first was said by G-d and the second by Moses and as indirect prophecy (it wasn't preceded by "וידבר הק אל משה לאמר" - he described the Decalogue in his own words.
The second is to whom they were said: the first was said to the Generation of ...