The cat, who doesn't have a name yet, has mellowed a bit. Still tends to follow me around, but less urgently. Seems disinclined to sleep unless I'm sitting still nearby, but did eat without my being in the room. I picked up some kitty litter and some food Wednesday night. Keeping her out of the bedrooms is a challenge (and keeping the door to the blue room closed screws up my attempt to keep other parts of the house cool), but so far things are mostly okay.
The part that's most not-okay is my breathing. I've lived with cats before, and have mostly just had to keep them out of my bedroom. But either I've become more sensitive or I can't cope with the combination of humid weather, pollen, and cat. Nothing dangerous yet, but uncomfortable. That might be the show-stopper.
(BTW, I haven't managed a definite identification of the cat's sex yet -- there's a whole lot of fur in that area, and she hasn't been cooperative in letting me get a look. So if I change pronouns in a few days, you'll know why. Her coat is interesting ... slightly longish shorthair on the top and sides, but the belly and tail of a shortish longhair. Confusing, but pretty. Now if I could get the last of the little green Velcro-burrs (if not the species that inspired the invention of Velcro, then something close) out of the fur....)
Haven't gotten up to the SPCA to find out whether there's a chip yet. A little nervous about leaving her along in the house all weekend while I'm in Virginia, while the situation is still so new. She has shown no interest in going back outside, though I can lead her out there if needed. I'm tempted to attach a note to her collar saying, "Is this cat currently being cared for elsewhere?" and kicking her outside for an evening or two to see whether an answer comes back on her collar the next day.
I'm behind on replying to comments again, and unlikely to catch up before sometime next week, but here are a few bits... Lap versus desk: accepts that suggestion for about thirty seconds, then wants to be where my hands are again; but seems to have decided that once she gets sleepy enough (which takes a while), stretching out at my feet is acceptable. Now I just have to make sure I don't run over her tail with the chair. Claws: something about the way she kneads did suggest "taken from mother too early" to me. Still attempting to teach that claws+skin=bad, but I'm not sure she's even aware she's using her claws. Doesn't seem to be dim; I think it's something specific about the kneading behaviour. Not very interested in playing; only seems to want company (and to be petted). Certainly not naming her until/unless I know I'm definitely keeping her (but tempted to use a variation of the name of the person whose phone bills I keep getting despite having written "never heard of this person -- return to sender" on the bills and collection-notices).
I wish I could have her curl up on the bed next to me when I sleep. But that would be a bad idea.