Now, about your ][gs and the JAMMA...
Marco Orlandi, <http://www.apple-iigs.info/doc/fichiers/Using%20Apple%20II%20AppleColor%20RGB%20Card%20with%20an%20Apple%20Analog%20Monitor.pdf>, has Pin-Outs for the AppleColor RGB Card and the ][gs RGB Port. His ][gs RGB Port Pin-Outs match yours..
I "believe" that ALL the Outputs are 0-5 VDC ( TTL ), so if you get the Wrong Video Sync, try the other one.. If Tying ALL the Grounds together seems to cause Interference, you might try using only One, possibly the Red or the Green..
I wouldn't connect the JAMMA Ground to the NTSC/Composite Output... I would think that Shorting the Output would not be a Wise Thing to Do.. Possibly the ][gs Uses that to tell it to provide NO Composite and Only Output RGB.... I guess I will find out shortly....
MarkO