You have gotten good advice here. A short letter letting Princeton know you are interested, any new developments and a short and subtle reiteration of how you can add to the Princeton community is the most effective thing you can do.
When it comes to challenges he’s, health issues, problems, these top schools Are only interested in these things if you spectacularly achieved despite those things happening. Any hint that they might be an excuse or reason is not well taken because so many have such stories.
Your stats and situation are similar to my youngest’s and I can tell you Princeton would have been a lottery ticket for him. No one in his school was accepted with those numbers without a strong hook. In your case, ithe professor for whom you performed, could have been a hook, but clearly he was not. I would not bring that up again. Certain things have to be brought up by others. It doesn’t come off well from the applicant.
You’re emotionally invested in the school so it’s a waste of time to say to forget about it, and move on. But , do move on. I don’t remember what other schools you have on your list, but some colleges do require focus and demonstrated interest to gain admissions. My son was careful to give each school in his list due attention , and I think it Marva difference in the results.