i think part of my problem with governor might be that i use its own trashing too much early - i just can't pass up the chance to turn an estate into a cantrip! i like never gain gold until i have a few governors and maybe that's dumb as heck???
If you're using Governor to remodel a card early on, you're helping your opponent pretty much as much as you're helping yourself, since they can almost always just thin a Copper. Drawing is the strongest Governor ability early on most of the time.
The big exception to this is when you're remodeling a Silver (or something else) into MOAR GOVVIES. In this case your opponent will usually have a tough time getting even close to the value you're getting.
As for gaining Gold, it depends very much on the other support the board has to offer. Many times it's best to spend one turn gaining and drawing Golds and buying like two Provinces or so with it (this number depends vastly on what your opponent's deck is capable of) and then the next turn remodeling a ton of those Golds into Provinces. Usually before this I try not to gain Golds unless I'm drawing a lot and that Gold is legit going to help me get more Governors. Giving your opponent a Silver to remodel into a Governor can be much more helpful than an early Gold to you.