Same SD card works fine on another Omega2+ so I'm less likely to think its the card. Supply voltage looks good as well, 3.45v (need to adjust regulator resistors to bring that down to 3.3v) That's a good path to check and more data sheet driven then my approach of swapping the cards and performing a functional check.
I saw that diagram with those pinouts as well but isn't EPHY_APGIO_AIO_EN set in software and not affected by the boot pins?
After a few hours of experimenting here the issue turned out to be a relatively strong pulldown on GPIO45. This was affecting a boot pin. Looking at http://plan44.ch/downloads/Onion-Omega2-Pinout-annotated.png and the MT7688 data sheet though it isn't clear exactly what the issue is. Measuring the module itself there is a 4.7k pullup to 3.3V on that pin, so no need for external strapping. Pulling that pin down would appear to be enabling JTAG mode, page 33 of the MT7688 data sheet fyi.
JTAG pins look entirely separate from SD interface pins though so maybe I'm close on the bootstrap pin issue but off on the effect? I still can't figure out why everything would boot fine if that GPIO45 was strapped low (overriding the 4.7k pullup) but just the SD card wouldn't be working......