First, I want to express my sympathies to all of you here who have a loved one suffering from mental illness. And my admiration for those of them who have managed to move forward w/ their lives.
Lucy, I'm another one who things you've done right by DD2. That's probably part of why she has finally come to the point where she is ready to live more independently. I know most of the credit goes to her and probably some of it to her therapist. But some of it goes to you, too, IMO. Good job!
I agree that you need to leave things as they are, for now, in case this first attempt at independence doesn't work out. She may move in and out a few times before she decides, once and for all, if she can make it on her own.
As such, I'm surprised that you've already spoken to a prospective tenant. I don't see how you could possibly know for sure by May - or any time soon - whether DD2's new situation will work out. IMO, it's not just a matter of whether or not you'd like living with a stranger (and I get that concern) or whether or not DD2 will be ok with someone else living in her old room (though, yes, it might bother her). To me, it's mostly a matter of whether or not DD2 may ask to move back in, at some point, or even show up at the door, with all her belongings, when you least expect it.
For this reason, I really think you need to table the whole "new tenant" idea for a long time, maybe even a few years. Hopefully, there will come a time when you can truly feel free to move someone else in if you want to (and I know you may not want too). But now, in my view, is not the time.