Okay, following up on what Marqs recommended, I have been able to program my Harmony with the NEC codes, and my OSSC does indeed respond to them by blinking the green LED as expected. If I understood Marqs correctly, that indicates that the FPGA may at least be booting, though the remote codes don’t yet appear to actually have any other effect and it still shows nothing on the LCD screen.
The replacement SCART socket I mentioned also arrived today, and I added and tested it to see if it produced any new behaviors. As with the component input, I got only blank video on the HDMI output. The SCART audio was correctly passed to the audio out jack, but unless I’m mistaken that’s just a passive passthrough, so it wouldn’t be touching anything relating to the unit’s main operation, anyway.