I haven't tried this, so I may be completely wrong. I suspect that the later model Singer RH12 lever wind backs do not fit on the RB67, probably causing trouble with the RB67's interlock mechanisms. (I'm fairly certain the earlier Graflex knob wind ones do not fit.) But I also suspect that the Singer lever wind RH12 insert will fit properly into the body of the RB67's film back. I know that the guts of the Singer 6x6, 6x7, and 6x9 Graflock backs are interchangeable and you can get them mixed up. So, if it does fit, then you would get 12 exposures on the roll with the Singer guts inserted into the RB67 film back.
Without it in front of me I cannot remember where the image masking gate is located (on the back's body or on the insert), so I don't know if it would overlap the image or not. If the mask is in the wrong place (and I think it is in the wrong place) then a bit of judiciously applied Gaffers tape will probably work just fine to get a 6x6 image gate. You could make some slight marks on the RB67's back to guide you in placing the Gaffer's tape if you have to remove and reapply it regularly in the context of the project. And you really ought to have a roll of Gaffer's tape in your kit anyway. It's wonderful stuff.
Proceed on this at your own risk. I have never tried this myself. But do let us know if you try and it works or doesn't work. More knowledge is better, even if it is the knowledge that it doesn't work and the next poor soul shouldn't waste the time!
It's probably cheaper than trying to find one of the rare albino RB67 6x6 film backs. And if it works it would let you use the same camera for both formats for the project.