If the sync off the JAMMA connector is 5V TTL or less, it should be fine; but the video output, depending on its fidelity, may benefit from the low-pass filtering provided on AV1/SCART, so don’t entirely discount a SCART lead with properly-attenuated sync.
If 75Ohm sync really doesn’t work on AV3, then I’m not sure that you can have a one-cable-fits-both solution, since properly attenuating sync to bring it into spec with SCART will bring sync out of spec with VGA.
Since it sounds like your homebuilt supergun has a SCART output that outputs TTL sync, I think it would be best to attenuate sync there, before it hits the SCART socket. SCART devices can’t handle TTL sync without risk (guarantee?) of damage, so it makes no sense to have a SCART socket with out-of-spec output. Do that, and you should be able to safely connect it to the OSSC or any other SCART equipment with an off-the-shelf male-to-male SCART cable.