Since you're not really sure that the Coppers will actually be depleted (there are 30 more Coppers than Curses!) really fast (Mountebank has its notorious diminishing returns), I doubt whether it's a good idea to aim for the Estates from the get-go.
Sure, if you see that there are only a few Coppers left, it's not a bad idea to switch into blind VP mode. By this time, your deck will be so fat that those Greens won't hurt that much. I think I would aim for the highest VP card I can buy at any given point instead of just Estates. The key is to be the first to notice this and try to build an unassailable lead. Others, in blind panic, will probably join in and actually help you to 3-pile whatever comes first: Duchies or Estates.
So I would, depending on the kingdom of course, try to build a deck that has decent buying power in the end game, plain old BMU can be helpful, because you only need 2 or 3 good cards in your hand to buy a Duchy. Then just try to buy (Provinces,) Duchies and Estates.
With the IGG-rush I believe it's not a big mistake to grab a Province if you're able to. The same probably holds for this example.