Are you sure it's WHITE smoke? That's steam (or, more properly, condensed steam in the exhaust). If it has a blue tinge, that's oil smoke, which would be either blowby or valve stem seals (or possibly an oil gallery leaking across the head). It sounds like there was no smoke beforehand, so it's due to the repair. When you replaced the head gasket the second time, did your pistons look unnaturally clean? You might. be able to smell antifreeze in the exhaust condensate -- kinda sweetish smell. There could also be some sludging in your engine oil.
The true color of the smoke is definitive. It's either oil or water and you need to know which to get to first base.