You're probably confusing "full ground" of "earth ground" (FG) with your local DC or video ground (GND). These are different things.
You do NOT want to connect FG/earth to the JPAC/JAMMA, so forget that.
GND will already be connected when you plug the JPAC into your computer, and the JPAC connects this to your monitor (probably a black wire).
As for vertical rolling, there are a few possibilities. If you can't adjust it into stability, or it seems to jump around a lot, it could just be a dirty or damaged vertical hold pot. You could spray some deoxit or other electrical lubricant/cleaner and give the pot a few turns to clear any gunk away. That might improve things. If the pot is really bad you could replace it. But then, it might be nothing to do with the pot.
Alternatively, look to see if your monitor has a separate vertical sync input. Check the monitor video connection plug, does it take five wires or does it take six? Five wires is composite sync, six wires is separate H+V. Colours are typically red, green, blue (RGB), black (GND), white (composite/horiontal sync) and yellow (vertical), though your colours might vary.
Point being, JPAC outputs combines the H+V from a computer into composite sync. AFAIK it doesn't output separate vertical sync.
So, if the monitor expects separate sync inputs, you could try connecting the composite sync to the vertical. It'll probably work, monitor can probably tell the difference. The horizontal sync pulses are quite short, whereas the vertical pulses are quite long. Better than nothing at least, and testing it won't blow anything up.
Quick and painless way to connect the syncs would be to get about 2cm of a paperclip (or similar), bend into a U shape, and slip it into the back of the video connector to short H + V signals such that it connects the metal wire crimps and shorts them together. If it doesn't work then it is easily undone.