While 0scar was right that cooling fan hurts layer adhesion, I've continued to have problems with PETG even with no fan, regardless of temperature. I went looking for advice on the topic, and found a video by CNC Kitchen emphasizing the importance of tuning extrusion rate because of the compressibility of the material in the extruder gear. I'd already found this was a huge issue with TPU and other flexible filaments, so it seemed compelling, and sure enough I just measured that a nominal extrusion of 180 mm only moved the filament by 173.5 mm.
OK. Having extrusion rate off by about 3.5% is plenty to make prints brittle with PLA - I've experimented with this before just to see what would happen. A longer more precise extruder calibration showed more like 4% error. After correcting this, things were better, but I was still getting severe brittleness in some parts of the print but not others.
It turned out the last remaining problem was speed. PETG does not like to be printed fast, and apparently part of that is not about needing a slow-moving nozzle to bond with the previous layer, because it wasn't the fast-printed part that was brittle, but the part printed immediately after fast-printed support structure. (One plausible theory for the mechanism of the failure here seems to be filament slipping in the extruder due to trying to extrude too fast, resulting in underextrusion.)
Reducing all the speeds (including support!) down from 60 mm/s to 40-45 mm/s seems to have done the trick. This is for 0.2 mm layer height. Presumably I could go higher with thinner layers, but I've heard PETG also doesn't like thin layers, so this is probably the sweet spot. Thicker layers probably don't make sense because they'd just require proportional slowdown, at least without a larger nozzle.
In the process I also tuned linear advance K factor for PETG, which seems like it might have been a contributing factor. I started with 2.0 which was too high, and dropped to 1.2 which was slightly too low; around 1.4 seems to be ideal. Having this too far off in either direction could/should impact layer adhesion as well, but only with prints that use widely varying speeds or if acceleration limits are very low.
TL;DR: Fan completely off, tune extrusion rate to account for compression of PETG in the extruder gear and avoid speeds over 45 mm/s at 0.2 mm layer height and 0.4 mm nozzle diameter.