I thought you talked about the L-1000 controls, but I thought it would be good to mention this. Your information is always thouroughly researched. I used some ot what you wrote above here for my news item about the G&L, so thanks!
There has been some confusion about the OMG position, and there may have been circuit variations over the years. There are G&L experts who know much more than I do.
The early instruction sheet for the switch called it “Single Coil mode plus added bass boost” but as far as I can tell, it was never single coil in the OMG position. Even in early examples that have been tested, the DCR in OMG mode is twice the DCR in single coil mode (center switch position), and there's no hum. It was later shown in a schematic as "series humbucking with .1uf capacitor."