Thanks to all who've replied. To reiterate what I said in my OP, to those who suggest keeping her out of the bedroom, I don't have a bedroom. I live in a studio apartment - a fairly big one, but a studio nonetheless - which means there are no doors except for one closet and the bathroom. I have no way to keep her away from the bed at all. So while I appreciate the sentiment, "keep her away from the bed" is kind of a nonstarter as far as potential approaches to the issue go.
The thing is, I don't think this is true litterbox aversion exactly. Because she uses the litterbox just fine when the bed's covered; she never pees on the carpet or other furniture. It's more like bed is first choice, litterbox is second choice if the bed isn't available - this is also why I don't think adding another box will do much to keep her off the bed, because she doesn't seem to be dissatisfied with the box she has, she just likes the bed better.
As far as a recurring UTI or something, no, we're absolutely sure she's over the UTI. The vet did a full culture - you know, where they call you in 3-5 days w/results - at her last appointment to be sure. And we really trust this vet, as my husband's family has been taking their six (at various times) cats to her for more than 20 years, so I don't think the vet is the problem. We've tried adjusting her diet to eliminate the risk of future UTIs by shifting to primarily wet with only a tiny amount of supplemental dry food (as opposed to currently 1.5 oz a day wet and half a cup dry), but she *did not* like it - she wouldn't eat all or even most of the increased wet food meals, and would try to lead us to the dry food bin because she was still hungry. We also tried switching her to a higher-quality wet food by mixing it with her current wet food, no dice there either. She seems to be quite set in her ways as far as food goes. >.< The best compromise we've been able to manage to help keep her better hydrated and reduce risk of another UTI is that when I feed her her wet food 2x a day, I add two spoonfuls of warm water and mix it together into a sort of "kitty jambalaya" as my husband calls it. Which she loves. So for now, we're just going to stick with what works. (Also we're getting a cat fountain to encourage her to drink more water as well.)
We had, for a bit, been praising and giving her treats when she used the box. I had thought that was enough, because she had gone back to consistently using the litterbox and we were just keeping the bed covered as a "just in case" sort of thing, so we stopped. I like the idea of using the crate as a training ground, but I'm not sure how to implement that, because her pee times are much more varied than her once-a-day poop, so I couldn't just crate her at certain times. Maybe...if we uncovered the bed, and I did the constant-vigilance thing, and then as soon as she jumped up and started to paw at the covers, picked her up and put her in the crate with the litterbox? Does that sound like something that might help her learn to reprioritize the box over the bed? (I'm thinking of getting a collar with a bell for her, too, so I can at least *hear* her when she jumps up on something, as opposed to only being alerted when she starts knocking things over or pawing at things.)
A friend from another site who studied animal behavior and behavior modification in college recommended I use clicker training to encourage her to play/sleep/eat on the bed while it's uncovered, to help her associate the bed with those things instead of with going to the bathroom. So I might try that too.
I'm sorry if I seem negative, I guess there *are* options still to try, I'm just...exhausted of dealing with this, considering we've been wrestling in some way or other with inappropriate elimination problems for about two months straight. And I know it's not really fair to her to be so upset with her about it, it's not like she's doing it to be spiteful (I don't think...), but just...ugh. :-/