Anyway, at first I couldn't find a service manual for the D501 online anywhere, even in the 13GB torrent of JVC manuals. I did find one for the D502 and it showed it had the same jungle IC as the Toshiba. Great I thought, maybe it'll be practically the same as the D501. I finally opened it up this weekend and wouldn't you know it, it is practically the same except for the jungle IC! It's got some JVC branded one which I couldn't find a data sheet for, of course. It's probably another manufacturer's but who knows which one. The micro was the same, however. I traced the RGB lines to the jungle IC, before finding a service manual for another TV that uses the exact same chassis but lacks the PiP daughter board that my TV has.
Looking at the schematics, I confirmed that I did indeed have the right pins. What was interesting was that I noticed the RGB going into the jungle IC was labled "mix RGB". It was routed first around an unpopulated header for Guide Plus (a late 90s early 00s thing like the menus you get with a digital cable box) then into and out of the PiP board. Ahhh, so what they're doing is using the same RGB inputs for OSD, Guide Plus and PiP and just muxing one on top of the other.

Testing the RGB input was as easy as pulling the PiP board and plugging the Genesis RGB into the connector, along with 5v off a regulator into the blanking ("YS") line.

Results were a near perfect RGB picture! I took some photos, but I wasn't satisfied with how those turned out TBH. I can try again later if people are interested. There's a purity or convergence issue in the upper right corner that I'll have to address but with no OSD being muxed by the PiP board I couldn't do it with the RGB input... or could I?
Long story short, I should have an LT1675 RGB mux IC Wednesday evening (with 10 more for $25 on the slow boat from Ali Express). It's actually made for things like OSD and PiP. Not only will this let me keep the the OSD overlaid with the RGB input, looking way more like it came like that from the factory, it means the 4PDT switch is no longer needed, since I think I can have the mux IC switch to overlay the OSD with the OSD's blanking signal. The LT1675 from Ali Express costs actually less than half of what I paid for my 4PDT switch too! All that'll be needed is a on/off switch for the 5V blanking.
PS - With this bigger set, I now see that my HDG non-TMSS Genesis does indeed have the dreaded jailbars. I thought I'd gotten lucky. I couldn't see them with the Toshiba and they're not that bad really, but now I can't unsee them of course. I'll have to take care of them when I re-cap it.