Finished with the plumbing and framing, I've moved on to wiring for my basement remodel, and I have a question about wiring receptacles. There are already many on the basement walls, about 6' off the floor, some of which feed first floor receptacles. My original plan was to re-wire these, and feed all of the ones to the new bedrooms and play room. Then I had a thought...

I now have a separate 15 amp circuit, 240v, wired with 12-2 w/ ground, which supplies a wall heater for the bathroom. Low amp draw with it wired to only 1000 watts. My wife didn't really want this, thinking that the boys would rarely use it. My thought was that I may be able to use this to feed all the new receptacles. I don't think I could do it with the 12-2 wire, no neutral. BUT... is it possible to use 12-3 instead? Then I think it could work this way:

Using 12-3 w/ground: black and red hot from the 240v breaker, white to neutral bus, and ground to ground. At the heater switch box: red to red, black pigtails to black and then feeds receptacles downstream, as do white and ground.

I'm pretty sure this would work fine, but I don't know if there are good reasons I shouldn't do it this way, both electrically and for code reasons. Also, if acceptable, is there any way to do it with 12-2? Any input would be appreciated.