Hey folks.
Unless I'm missing something I think you are making this way more dificult then it has to be. Take this with a grain of salt because I'm no expert, I have more expeirence with video prod monintors then arcade ones (and please if I state something that is absolutly wrong, correct me).
BNC's are just connectors, the inside pin will be the red/blue/green/sync and the outside edge will be a ground, sound familiar. The video coming off of your JAMMA card is also broken into these, except you usually only have 1 ground. So to hook this up you could either open up the monitor case and solder some cables directly where the connectors are (not exactly a fun thing to do) or make a set of BNC breakout cables and wire these directly to the wires in your JAMMA harness (not too dificult a thing to do, but remember to send all of them ground). Take a look around at electronics stores either brick and morter, or online and I'm sure you will fine the conectors you need. The other advantage of making the cable, is it's easy to disconnect, and yet is a very solid conection that won't just pull out.
The only part you may have to do some exprimenting on, is what the sync actually is; horizontal, vertical, combined and wether it's positve or negative, and that's the part I'm clueless on. But you may get lucky and have it set up to match your card right away.
Best of luck,
John