I removed the test mentioned in the TMS1100 data sheet - only updating the R-Latches if the X Index register was less than four.
It partly worked - except it came out back to front and upside down. Turns out that the LCD input was reversed, which I fixed by reversing the bits on the LCD driver (equivalent to reprogramming the Parallel Output ROM to do it), and as you can see it works well enough.
Hitting a few keys at random it appears to do what the BlockBuster Cartridge does (haven't checked this properly yet), and it also starts up the game and displays the initial wall.
I wasn't, originally, going to emulate the Rotary Hardware, but perhaps I will now, just to see how it works.