For what it's worth, I wouldn't send another round of letters to everybody, for a couple reasons.
1. Not that you're not wonderful and don't DESERVE all positive reviews (because I'm sure you are and do), but you don't actually know that everybody's review of you was positive, and a letter presuming that it was is a little, um, presumptuous.
2. It seems a little over-eager. Normally I'm all for over-eager, but a formal thank you again see you soon note seems excessive. Definitely stay in touch with the POI, but the others... maybe a quick email, thanking them again for the interview and saying you'll be seeing them in the fall. But not the whole hand-written note thing.
But that's just me.