I'm not looking for specific advice for how to play as Player 2, but those are further examples of how the first player has an advantage.
Suppose there are two Provinces left (each player has three), and both players are on what is likely their final shuffle, without any +Buys. (The same principles generally hold with them, but let's simplify this example.) If Player 1's next turn reaches 8, he can buy the Province, so that Player 2 is racing to buy the final Province before Player 1 does, and they'll each buy Duchies and Estates in the meantime. As long as Player 2's deck is roughly as good as Player 1's, they have a very good chance of tying, but are much more likely to lose than win.
However, suppose that Player 1's next turn reaches 5, and they buy a Duchy. If Player 2's next turn also reaches 5, that's fine, they match Duchy for Duchy. However, if their next turn reaches 8, they have a terrible dilemma. If they buy the Province, then Player 1 just has to buy the next Province before Player 2 does, otherwise trading Duchy for Duchy, or even falling behind to one Estate, for a victory. Not guaranteed, but also rather likely if their decks are similar, as Player 2 just drew a very good hand, and is unlikely to get that same buy power until the next shuffle. If Player 2 instead buys a Duchy specifically because of this dilemma, then they had to underplay their hand. If Player 1's next draw reaches 8, they can buy the next Province, and Player 2 still needs to catch up as in the previous scenario, but they already drew a hand that reached 8, and are less likely to be able to replicate it in a future hand.
Granted, this is a slight simplification, as players can also get unlucky with falling just short with 7 or over-extending to 10 and beyond, which will also make future attempts at 8 less likely, but the general principle holds that when the game comes down to the Provinces, Player 1 has a clear advantage and the tie-breaker, which is effectively half a point for Player 2 if there's a turn imbalance, is not sufficient.
I'm curious to know what the stats are from online 2-Player games for how often Player 1 wins, particularly if you only look at games that ended with cleared piles instead of an early resignation.