Man, I think you've been getting some bunk advice.
It can't be the boardset, since you tried a seperate one.
It's definately in the monitor.
This setup was designed for two monitors as well, so there's a part of the board that drives the menu select that on the two monitor goes to the top monitor, and a seperate part of the board that drives the gameplay, which goes to the bottom monitor.
On your 1 monitor board, they must have redesigned it to output to the same monitor, but now it switches back and forth depending on if it's showing the game select screen, or the gameplay screen. It's still likely using two parts of the board to produce the same screens, just having the roms redirect the two images at different times.
SO, what I'm saying is, two different sets of signals get sent to the monitor. All the 1 screen boards do this, that's why you had the same problem when you swapped the board.
Your problem is your monitor is adjusted wrong. It's just BARRRRRELY in adjustment, as far as the Horizontal Frequency goes. When it swaps to the select screen, it sends a slightly different sync signal, so the monitor is right on the edge of being adjusted right, and then falls out of adjustment when it switches.
Wait till it goes crazy on you again, and then adjust the horizontal frequency; NOT the horizontal center! Thats' not the right pot, there's a pot sticking straight up off the board just behind the flyback that is the horizontal frequency pot. Look where your cage is around the flyback, just behind that is the horizontal frequency... wait till it messes up, then fix it with that knob and see if you aren't in business.