So then, how do you deal with that situation? It seems like Mountain Pass can bring the game to a stand still if no player wants to gain the first Province.
I don't remember if anyone ever came up with a solution other than trying to beat that with a non-Rebuild strategy.
That's still rough, because the Rebuild player likely won't have a problem bidding 40. But unmirrored, there should still be Duchies available for the non-rebuild player.
That depends on what Rebuild player does. They are going to nab 3 Provinces for a point total of 26. They will burn 3 Duchies in game so total points left are only 45 outside of estates. If Rebuild gets an Estate before the trigger is pulled on Mpass, this pushes their total up to 32 and drops the opponent down to 34 (at best). It is exceedingly hard to beat Rebuild with only the stock VP when they can take 8 and run. It certainly can be done (e.g. Knights)
The solution for the mirror is to win the Duchy split, then buy Rebuilds and Estates. Name Duchy, burn Estates, and then slowly eat the Rebuild pile. If your opponent gets a province - bid 40. If they never touch it, then you just keep eating the piles. Be careful about the Estate count; a 4:3 province lead means you cannot let them get 3 Estates ahead of you. If you lock them out of Duchy or Estate points, then you just wait for them to name province, net your 8 VP and then name Estate.
Losing the Duchy split is pretty fatal here, but it is in many Rebuild games regardless; you can get insane mileage out of Rebuilding Duchy -> Duchy.