My strategy against a Herald deck would be: Buy Governor every time, even with $6 or $8, until they are gone. When playing Governor, only Remodel if you can get another Governor, otherwise, gain a Gold (ocassionally draw depending on tactics and shuffles, like having 3 Governors and nothing else on the deck and wanting to prevent them missing the reshuffle, or doing the opposite to the opponents). After that, just remodel into Provinces and draw a bit more aggressively. When the opponent start using my Remodels to their benefit is too late. If the opponent is using the Silver to buy Governors, the Heralds won't help them a lot and he is basically mirroring, but starting later.
If the opponent still did not build up enough after Governors are gone or almost gone, maybe buy some Nobles to have extra draw and finish the Provinces in two turns maybe.