This turned into being a tricky one..
Got this one from a friend to get working again. We had discussed the symptoms and in the past, this has been caused by the LS42@H3.

It boots directly to a screen full of dots with two little pink squares in the middle. He replaced the LS42@H3 - but in this case it was not the issue. If you look close it also has two rows of dotted lines at the top.. I've never seen that..
Knowing that this was caused previously from Pin 3 and 4 shorted on the LS42 ..

I followed the pin 4 output to the LS32@E3.. Pin1 and Pin2 inputs were good.

Pin3 output - not good at all. My friend had checked it with a logic probe.. He really needed to pull out the scope! Game boots now!
However..
This issue I chased for a while. At first it seemed thermal because it would 'ram up' with time. But that was not the case, the colors would change after a time..
I looked at the horizonal output part of the schematic, but it moves ascii characters around and this seemed later in the circuit. One thing I did was just remove the character ROMS@F7, H/J7
Another helpful moment and trick I found was to shut it all off. I pinned the
MATCH line to 5v+ and shut off everything(?) in the graphics circuit.
Still getting video noise with everything shut off (I believe). Color mapping could be hiding stuff in theory..

I poked around here for a while and tried to see if I could back trace the noise.. Pinning the
MATCH line high did shut off most of the data coming into this circuit. The address bus lines were the only thing really doing anything. One item of note early on - The game had a 6502, not a 6502A. I had put in a 6502A - at the time it didn't make a difference.

I had been back to these two LS244s a number of times. I did Slice and signature analysis on them and they were good. But I happened to piggyback the LS244@B1 and all the noise went away?!
Replaced it and it is still gone. I'd replaced a couple of chips that seemed to be involved only to have them not have any effect. Oddly - I put the original 6502 back in and the trouble returned. So 6502A it is.. Root cause is likely some impedance, noise or timing issue ? Nothing jumped out and I checked each pin. I followed all the lines coming out of @B1 and they seemed ok.
Adding to the complexity - the PCB does not completely match the schematics. I looked for a different revision, but could not find one. Learned more about Centipede for sure..

I gave it a good workout, Board works!