How can you get around the lack of early stone in two-player Agricola?
As far as breaking the game goes you'd have to experiment. Since those cards don't always come up it's hard to say with out play testing how early stone would affect a 2-player game with and without those cards. 

My suggestion would be to as you say accept the limitation and use the draw 10 pick 7 method for Minor Improvements and Occupations. That way if you are playing a 2-player game and draw a great card but it requires stone you can decide not to keep it.

Ultimately house ruling things is about having more fun, so if you add a path to early stone for 2-player games and it's more enjoyable for everyone then go for it. That said, in my opinion, Agricola shines at making you feel like you never have enough time to do stuff so removing that from the game (even in a small way) diminishes one of the core qualities of the game.