1. A3!!
What's the problem with 1...e5?
Sorry but this is wrong.
1.a3 's idea is not to transpose into Sokolsky's 1.b4, but to transpose into other openings like :
1.a3 d5 2.d4 : Queen's gambit where a3 can be useful
1.a3 e5 2.e4 and here, hoping a3 will be useful.
Sure a3 can be useful but then : why almost nobody plays 1.e4 e5 2.a3, or 1.d4 d5 2.a3 (which is quite ok, GM Prié used to play it a lot with very good results)?
Personnally, i like to play 1.a3 Nf6 followed by g6, playing a KI set up where a3 is irrelevant.
As white, i quite like playing Gunsberg variation on 4 knights : 1.e4 e5 2.Nf3 Nc6 3.Nc3 Nf6 4.a3, which is rather venomous... But i d'ont begin with 1.a3, black having plenty of ways to play it.
Noble attempt, but black can simply play ...f6 in addition to ...e5, shutting down your bishop and having you waste 3 moves in which you seriously weakened your position and didn't accomplish anything. For example:
If you really want to play b4 with a3, there's no point in playing a3 first. If you do, you have to decide what to do when black plays g6.
As for the variation with f6, I believe Be6 first is better, IIRC. e4 is already protected and Be6 would prevent c4. I know this is one of the main systems against the reverse... 1.d4 b5 and 1.e4 a6. The only time I've faced it, I've treated it like a gambit rather than end up with the setup Spassky had in the opening after this game:
Maybe being up a tempo, black wouldn't have time for a5 to force c3 instead of c4 but it still seems like white's ideal setup has been thwarted.