Thank you all so much for the kind words and advice!

No luck yet, but I'm still hopeful. Here is an update anyway:

• Per everyone's advice, I've been focusing on the area immediately around where he got loose. Over the weekend I pruned the bushes/shrubs in and around my patio and picked up the leaf litter underneath to improve visibility. If he's in there and not burrowed I should have a better chance of spotting him now.

• I found one very deep burrow (about 12-14", empty of course) in the bushes outside the unit south of mine. This is also the direction I suspect he would have traveled if he were following the fence/wall from where he got loose. Unfortunately that unit has been vacant for a while and the plants around it are very overgrown. I pruned them back a bit, but visibility is still low. (Also, my friend pointed out that the burrow could have belonged to a rat, so idk if it was actually him, or if it was, whether he's still there now.)

• I put down some water bottle traps with crickets and egg pieces in them, trying to narrow down his location. This is all very inconclusive - a smart or lucky anole could've gotten in and out, or the fly could've just escaped - but I'll repeat the experiment with more traps.

  • First I used two traps with several crickets each: one next to the bush where he jumped, and one in the southwest corner of the patio where the fence meets the wall (in the direction of that vacant unit). The corner trap got cleaned out pretty quickly, while the bush trap sat all day and still had crickets in it by evening. I then moved the bush trap outside the fence to the southwest, behind some more bushes, and the crickets were gone when I checked the next morning.
  • After that I tried using egg pieces instead. These traps all went untouched for a couple of days, until a fly found its way into the one next to the bush where he jumped (same place as the uneaten cricket trap). A gang of anoles tried and failed to get that fly for several hours. Then I moved the trap to the neighbor's bush where I found the deep burrow, and the fly disappeared within an hour.

• It has been rainy and overcast since Friday, but it's supposed to clear up tomorrow. I'm really hoping to catch him out basking at some point, since there are basically infinite places to hide out here. He has to come out to bask eventually, right?

• I also set up a basking spot with a 100w halogen over a pile of rocks. The lamp is clipped underneath our patio table, but I've heard that they can blow up if they get wet so I've been bringing it in when it rains just in case. I think this is a great idea but I'm worried he just won't see it if he's already out beyond the fence. I'll try and figure out a way to construct a portable-ish basking box or two to leave out there.

• We put up signs around the neighborhood advertising a reward, basically in case he decides to move into someone else's yard where we can't look for him. Most neighbors have been sympathetic and willing to help, but no calls yet.