Nick,
Pardon my late reply.
I've thought about this on and off for about five years.
Yes, it's certainly possible. It merely needs a 12V to 36-0-36V DC to DC converter. These things are not too difficult, but they require purpose built magnetics, which can be elegantly sidestepped with a dual 120Vac to 40-0-40Vac toroid working backwards at lowish frequency, say up to about 1000Hz. This can actually be made very economically using special chips, but there's a bit of R&D in it. The idea of using a mains toroid backwards is not new, but it means costs can be reigned in considerably.
Cheers,
Hugh