A few updates. First a caveat: I am not an electrical engineer, so I might be jumping to the wrong conclusions.
I’ve pared my test setup down to the minimum: the TC mainboard (without display) and an external power supply. RFI still causes all three fault types (quick reset, slow reset, hard off). Leaving the board alone for 10-100 minutes pretty reliably yields a quick reset.
I’ve checked for any obvious solder or connectivity issues and can’t find anything. It’s still possible that my TC is defective in some way – in fact, I hope it is, because then a replacement would address this issue!
From reading about rp2040 hardware design (see https://datasheets.raspberrypi.com/rp2040/hardware-design-with-rp2040.pdf), I’m starting to suspect the distance between the rp2040 and the flash chip might be an issue – it’s called out explicitly in that document. When I used a scope to probe the flash QSPI control lines… it looked pretty messy (again, I am not an expert!):