Just don't do it. It's like taking a child from you. Someone else starts to bastardize it, use it in way you don't like etc. And you can't do anything about it, since it's not your thing anymore. I've made this mistake once and it's not a good feeling. Better bury it.
I mean, if it were some super unique thing, then sure I think there might be a some reason to suggest he should open it up.
But nothing about the site is actually technically unique beyond the brand and its history. It means a LOT to OP sentimentally, but if this was doing some kind of amazing social good, someone could just go make a rails app for their CS degree's senior design class and we'd have a functional replacement back.
So, I think OP's decision to bury it makes a lot of sense. It's a very human decision and it doesn't really hurt anyone by him making it, and if you want to be super utilitarian about it, it's probably better to let them peacefully close this chapter and move on to whatever next interesting thing they're going to do rather than sour them on it and have them do their next thing more privately.
As a counter-point, you built this thing in part to give the world something good and uplifting. If you kill the child, you guarantee the outcome of failure.
Sure there's a chance that the person you pass it to goes in a direction you don't like, but there's also a chance it goes on to magnify it's mission. It's such a neat project and something I wish I'd discovered before today (sadlol).
Hell, maybe I'll take it over if you're willing. I'd keep you access to it and grant veto power over any changes you don't like. What's the current stack? LAMP or something else?
Have you considered making it into a software package?
You could take any custom code you wrote (like the layout of the pages) and make a guide on how to remake your site from scratch (what software packages you ran, OS, things like that) and post that to github as open source.
That would allow you to keep your baby but then let your electric grandchildren float off into the internet to see where they might sprout.
Another thing is if you decide to bury it, do not burn any bridges. A few years later you might want to restart it. So make notes, keep everything archived.
I’ve felt this way for a considerable time too. In retrospect, it has now been ten years and yet still nothing has really changed, which I am kinda glad.