My 250 was 6v stock, but the later year 350s were 12v. I went to the local wreckers and got a 12v stator from a TT350 and installed it.
I had also thought about getting another 6v coil and wiring it in series with the coil already on my bike. It wouldn't be able to put out as much power as the proper 12v coils I got, but it would be enough to run lights, especially if they were LEDs.
Yes, LEDs do work quite a bit better on DC. They'll probably flicker on AC.
It's not too difficult to get a 12v regulator/rectifier and wire it up so you have a DC circuit. I changed my headlight/taillight over to DC, as well as replacing the taillight with an LED unit (the stock rubber mount fell apart on me during a trip I did).