+4.87v is plenty good enough for that board to run.
The +12v is only for the Audio Output, which will also run fine at +9.43v.
My machine has low +12v also, not a big deal.
Try flipping the switch that's located next to the fuses so that it points away from the fuses. See if that helps your voltages.
It shouldn't make your Game PCB have graphical issues, though.
You can't pull the transformer for the monitor out. You can pull the 9V transformer out, and replace the +5V & +12V with a switching power supply and a custom wiring harness. You would pull AC from the Line Filter, and wire the DC voltages to the correct pins on header 12P.
(again, this might not solve your graphical issues. you should test this before puling the transformer and hacking up the original wiring.)
EDIT: Now that I think about it, mine only has one transformer with two windings. It does both the monitor and the 9v, which means that you can't remove the Transformer anyway. You can bypass it, but you'd need to find another spot for the switching power supply.