Ok, now you got me wanting to do some poking around...... because from your "working" video it appears you have the video input on the Sharp monitor connected to the INVERT OUT side of the Inverter Board. Which is primarily for NON-Nintendo games....in which case does indeed require power in order to work. But that would also mean that the signal from the board wasn't inverted to begin with.
But on the Sanyo you have there working the video input is plugged into the NON-INVERT OUT side of the Inverter Board.
That just doesn't equate to me.
One is one way and the other is the other way.
They should be both the same I would have assumed.
I'd almost bet if you swapped the video inputs from your game board to each monitor the colors would be screwed up again on both monitors.
Did this up awhile back.... good for reference here and there.

On a side note: Could you take a good regular pic of where that "12v" is coming from on the Sanyo? Like in your first pic. (the AB line) I need to add that wire to a Sanyo monitor that didn't originally have it and I don't have an example to go by.