A Moogle  🏳️‍🌈 💻 🎮 🎶 🇸🇪

What do they do? Looks like the board generates screen addresses in sequence or something like that for the display? Are the PROMs to change the resolution between regions? (I remember studying a Q*Bert service manual once, and the display board looked a bit like this!)

Depends on the board. For example, there's an entire card called the "Store Address Card", which has various registers including ones for the cursor X and Y positions. Rather than being directly mapped, the cursor X value is run through a bank of PROMs.

Ultimately the purpose of MAME is to serve as hardware documentation, and to an extent a way of helping people with bit-rotted ROMs burn new ones, so I'm trying to go as low-level as I can with the Paintbox, short of just chucking the entire thing into MAME's netlist system.