Well, that was easy. Got him first try with no trouble at all.
Tools used: Tomahawk drop trap + matching transfer cage. These are outrageously expensive; when I got the droptrap I thought it'd be easy to put a carrier up against the opening or something; I tried this on a different cat and it did not work. So. Transfer cage it is.
A drop trap is what it sounds like; a propped-up cage that drops on top of the beastie to trap them in a box. It's quite large. These are good for cats who might be wary of the more typical trap; rather than crawling inside of something, they just walk underneath. It doesn't "seem" like a trap in the same way. You attach a string to the little stand and give it a yank when the target cat is eating. The typical havahart (or whatever) trap has a pressure plate inside that slams the door shut on them, and these can also be rigged to shut manually. Those work just fine most of the time. In our case there are so many cats in the neighborhood - along with squirrels, birds, skunks, raccoons, and possums - we need something manual.
Well, I say "we", but I'm the one who does 99% percent of the cat stuff here... but it's my housemate's house, and they bought the transfer cage.
We did borrow a normal trap for this, but it's just a little too small for the gellow, so droptrap it is. My visual-spatial reasoning is very poor and I really struggle to translate written measurements into a concept of size, and I want to get him inside on the soon side as the temperature is starting to dip.
Wet food went in a paper bowl on the porch under the trap - since cats freak out when trapped, I've been advised by the local TNR people to never put hard bowls in traps so they can't hurt themselves with it! Especially not breakable glass. Paper is better. Not dangerous if they slam into it or throw it around.
He actually watched me set up the trap, just sitting a small ways away... I was worried that would mean he'd leave, but nope. I put the food in and then walked past him to the driveway and he only paused for like a minute or two before heading right into the trap to chow down. It's hard to tell whether the tail is fully under the trap or not from the position I was in, so I waited until he curled his tail towards himself and then pulled the string.
Getting him into the transfer cage was a bit harder; once the trap went down he started yowling and spinning around and rolling and was generally very upset and confused, and once the initial startle wore off he just wanted to hunker on the opposite side and cry. Sorry, buddy... but B got some treats and catnip from inside and I dropped a bit into the transfer cage, and that did seem to tempt him in. (He likes food.)
I loosed him in the basement and we spent a few hours sitting down there. I've gone back down a few more times, too. He's pretty upset, but not too too bad I think. Hard to tell. He explored a bit and sniffed things before deciding he wanted to hide behind a pile of stuff, and then stayed there for a good long while in silence. He did eat at some point when he was alone, and after that he started intermittently crying - I guess it emboldened him or gave him some energy?
He's stepped out of his hiding spot a few times and then backed back into it while I was down there. I walked over to talk to him a couple times and he responded with more awoos and some hissing. He didn't get puffed up, though, which I think is a good sign, and he did look on with some interest when I wiggled a toy around.
I've decided to have the basement lights on for him during the day and off at night, so he has some light cycling - I don't know how much cats care about that, so this seems like a good compromise? I've also decided to have food down there for him even when there's not a person there. Most of the cat advice things I saw said to have food available only when a person is there for socializing a cat, but that seemed too mean to me / not helpful in this type of situation. I'd rather he adjust to the space and feel like it's a good place to be where there's food when he wants it and he has everything he needs, no strings attached. I think that's more comfortable as an introduction. Once he's been here long enough to settle in and I can see what his "neutral" is and get a sense for his personality, then I can figure out what type of socialization stuff he needs.
The basement is quite warm - uncomfortably so for my taste, but good for B and hopefully for the cat as well.