There's a specific branch of flashrom for this setup. I switched to it and tried it, but the results were the same. It looks pretty old.
There is a quirk going on where the wiki says the new serial firmware is supposed to get 2Mbaud, whereas it's only communicating for me with 11kbaud, but I may have missed something.
I added some debugging output to flashrom and saw the chip manufacturer and id are reading as 0xFF both, as is data. When I glanced at the detection code earlier with the oscilloscope, it was inverting the data read, so 0xFF may mean the data lines are simply not powered.
Something I could maybe pursue next might be using the scope to see if any pins on the chip are outputting anything at all.
I could also try poking at the clock pin more. Even if it's quirky, it's good practice getting comfortable with the scope, and maybe I can learn the quirks.
Might also be meaningful to look up the sample rate of this scope and see if using a pi or an arduino as a logic analyser could increase it -- seems pretty unlikely though. I'm thinking an RTL-SDR would work as a high-rate logic probe, but I may be way off base.