Quote: "Edit: Googling shows that significant hardware changes will force me to reactivate my XP, but I can't find out whether that means it'll refuse reactivation. "
You don't really need to worry about that. Worst case, it will tell you that license is already in use. Then you just need to do the phone call option. It's painful trying to type in or say all the groups of 6 numbers, but once you do one of three things will happen.
1) It will activate and give you more numbers to type in.
2) It won't activate, and it will forward you to a real person (you will have been talking to a robot all this time)
3) It won't activate and hang up on you. In which case, call back, put in all 0s for the number, and it will get confused and send you to a real person.
Once you've got the real person on the phone, explain that you had to make significant hardware changes but it's still the same computer you were running it on before, just reinstalling. Then they'll give you a bunch of groups of 6 digit numbers to activate, and if that doesn't work they'll just give you a whole new product key.
They're fairly lenient about it. Once I tried to reinstall XP Pro on my girlfriend's desktop, and it kept refusing the OEM key (I had an OEM disc). I called them up and went through that whole procedure and they ended up giving me a whole new key. It was only later that I realized that it was an XP Home sticker, not Pro.

I'm sure getting a free upgrade is a rare case, but it's a pretty good indication of how far they'll go if you spend enough time on the phone and are polite & reasonable about it. We used to have to do this all the time when I fixed PCs at Circuit City.