Her is an article from 2005 that might be the first to explain why you should almost always go for 2 when down by 14 late in the game ...... he uses 43% as usual success rate on 2 point conversions (it has varied from 40-50% in college over many years) and 94% for one point conversions (was 96-97% in 2016 in college) ...... he explains his reasoning in detail mathematically and derives formulas that can be used ..... it's much of what you said only even more detailed but pretty easy to follow.
At the end of the day, he shows, just as you pointed out, that if you are down by 14 late in the game, your best chance of winning is to go for 2 points after the first TD then decide what is best after the 2nd TD which makes it more significantly likely you will win then if you kick extra points after both TD's (or go for 2 after the second TD if you miss the extra point after the first TD), and the worst chance of winning is to kick an extra point after the first TD and if you make it, try a 2 pointer after the 2nd TD ...... there are only a couple reasons not to go for 2 after the first TD and they are EXCEEDINGLY RARE.... Check link below ......
https://thesportjournal.org/article/playing-with-the-percentages-when-trailing-by-two-touchdowns/