OK, so my DSP4000 passed all diagnostics with flying colors.
Then, out ot curiosity, I put its SRAM card into my TC Electronics GoldChannel and it hard-froze the unit (several times in a row, actually) – dodgy SRAM card! Off to the bin it went.
I did a clear setup and internal RAM format on my DSP4000 and left it off overnight without a card in (I usually left a card in the unit) and it boots properly every single time now. It even boots with the other SRAM card inserted. (However, that card seems to be dodgy as well, as it throws a checksum error on the DSP4000 every other boot and shows up as 4MB on my GoldChannel even thoiugh it's a 2MB card.)
I've rebooted my DSP4000 about 30 times over the weekend and it booted properly every single time. Needless to say, the dodgy SRAM cards landed in the bin, and I'm off to making music!
Hope this information is useful for someone troubleshooting a similar problem in the future 🙂