Maming that cabinet would take a lot of effort, you'd have to gut pretty much the entire machine. Also note Popeye is a horizontal game not a vertical one so you couldn't easily drop in a x-n-1 pcb either. Well I think they do make like one horizontal one, but you'd still have to worry about modifying the controls plus the monitor issues.
Anyway as far as i can tell from those pics i'd still suspect the PCB over the monitor. The monitor isn't going to screw up in a way that makes random sprites dissapear, at least no monitor screw up i've ever heard of. When the graphics start going glitchy your problem is likely PCB or Power, not the monitor. Monitor issues are pretty easy to spot. You'll also notice EVERYTHING will be affected the same way, ie the entire screen will be the wrong color, or black, or whatever.. not just pockets of it.. typically.