I fried 2 Genesis systems and gave up for a while, but I discovered that a similar encoder circuit exists in PS1 systems. I managed to make a working hack today with quite satisfactory video quality, so I just wanted to show off...er...share, since half the cost of building a supergun is the RGB encoder, and this is how to build one for dirt cheap.
The PS1 core unit was given to me as a non-working system for FREE. All I had to buy was a digital controller, a DB-9 male connector, and a DB-9 plastic cover (the AC and A/V cables are the same as a PS2). Altogether this encoder came to about CAD$8. Pretty good compared to USD$78 for the JROK plus another CAD$10 to enclose it nicely with a box and external connectors (not to mention border duties for the JROK).
There are many hardware revisions of PS1, so I can't guarantee the motherboards will look the same. But look for a Sony chip that has a number like CXA1645 or CXA1145 or something. Typically it should be close to A/V out socket. Mine was an early weird model with the chip really far away.
You will need to cut the RGB and sync lines from the PS1 itself and feed in your own lines. Starting from the IC, trace the RGB lines past the first capacitor and cut the lines there. You can cut the sync line right at the IC. This is the hardest part since you might have to trace lines to the other side of the motherboard and the traces are very complicated. Audio was easier since I soldered it to the mobo right at the A/V connector. I didn't even bother cutting the audio from the PS1, since it only makes sound during bootup, and then is silent while it idles at the dashboard.
After soldering in your own lines to where you cut the original ones, you need to connect them to your supergun somehow. I didn't feel like doing any external modification, so I found a way to feed in through the P1 controller port. It costs a controller more than simply using another DB-9 socket, but I HATE having to mount DB connectors. So I just disconnected the controller board ribbon cable and soldered the video and audio lines to the controller board. Chopped the cable off the PS1 controller and stuck a DB-9 on the loose end.
There is also video ground, which I connected straight to ground on the PS1 mobo, and audio ground. Audio ground is a weird one. At first I also connected it to ground but it was causing interference with the video. I disconnected audio ground completely and now both audio and video work fine.
Here are some pictures..
Underside of the mobo. R, G, B, video ground, mono audio, and audio ground (ignore the light green one, I ended up disconnecting it).
Top of the mobo, with composite sync connected straight to the IC. Hacking surface mount ICs is pure Hell.
Mobo and controller ports screwed back in place, and power restored to the mobo from the power supply. The CD drive is completely disconnected.
RGB input through the controller port.
Woot! Looks decent through composite video. Pretty damn good with S-video. The colours are a bit bright though.
So that's all... It's certainly not an elegant or pocket-sized solution like a JROK, but it was only about a tenth of the cost. If anyone's on the fence about going JAMMA but worried about cost, I hope this helps...
I am to to mod a PSOne like that!!! 
, at least for Progear. 
