I found a few more problems with the board. I had tied the RAM WE to the cartridge, but I connected it to the flash ROM's WE which I think was screwing it up. I cut that trace, and then put pullups on the /WEs to the flash ROMS. The flash ROM then starting putting out the correct data. And right after that, the small test program started to correctly branch and go around the short loop.
However, I checked the load instructions and that is not working. I checked the input and output at the /LD gate, and the input is not toggling. However, the ROM diodes which feed into the gate are toggling. I checked connectivity and for some reason the trace is not connected from the diodes to the chip pins. I checked the layout and it is connected correctly in CAD. Looking at the trace looks good too. But I ran out of time again, so it's a problem for tomorrow. So close for the first test program running!
update: I found the problem - when I had to reverse all of my diodes, one of the traces broke right at the pad. I had to use the high power microscope to find it. So I just scraped some solder resist off of the trace and soldered to it. Connectivity restored! I'll check the functionality later today.