regarding 3. d4 I have no comments. I have neither played nor studied this move. I have always considered it ugly looking. I am perfectly willing to accept black is better after it.
Regarding 3. a3 I think white is fine.
You gave
1) 1.e4 c5 2.b4 cxb4 3.a3 d5 4.exd5 Nf6 5.axb4 Bf5
2) 1.e4 c5 2.b4 cxb4 3.a3 d5 4.exd5 Qxd5 5.Nf3 e6
I would remark that the mainline is certainly turning into 2a with 5... e5 instead of e6 where both 6. c4 and 6. Bb2 have gained popularity over the terrible line 6. axb4? where black is obviously better. A sample would be 6. c4 Qe6 7. Bb2 Nc6 8. Bd3 Nf6 9. 0-0 Bd6 10. Re1 0-0 11. axb4 Nxb4 12. Bf1 and I will argue this position is dynamic = with major chances for both sides. I believe there has already been a pretty extensive thread on chesspub on this line in the past.
But okay on to your lines.
1) I admit to never having seen this Bf5 move before. Indeed I can't even find any games with it played. It is a very strange move indeed and I can't believe black would be better after it. Initial CM moves are obviously 6. Bb5+ 6. c4 6. Nf3 I think White has real chances to prove a theoretical advantage here. He has all his trumps from the normal wing gambit (open lines, active pieces, full center control) with none of his weaknesses (pawn deficit and lack of control on d4). Lets just say for sake of argument 6. c4 as it seems most natural? I'm sure at all what the hell black is supposed to do? Nbd7 Nc3 and white must be better here without a doubt. e6 is plausible but lets say. Again white has a wide range of totally playable moves 7. Nf3 7. Ne2 7. Qf3 7. Qa4+ 7. dxe6 lets just say 7. Nf3 as i'm fairly certain white can't be worse here after say exd5 8. Nd4 Bd7 9. Nc3 Bxb4 10. cxd5 0-0 11. Be2 Re8 12. 0-0 is just = and of course none of this is forced white has so many pleasant options in the above for = that I just can't believe in Bf5.
Okay anyways we can discuss this further but I'd like to hear your thoughts behind Bf5 first.
On to line 2. I think again this isn't most testing but certainly black can't be worse so lets see white has all the normal moves 6. axb4 6. Bb2 6. c4 plus now a few more options 6. Be2 6. d4
I mean we can try and analyze all of these... but my first thought was 6. d4 so i'm gonna start here. I think 6. d4 Nc6 7. axb4 Bxb4+ 8. c3 Be7 9. Bd3 Nf6 10. 0-0 0-0 looks again dynamical equal to me with chances for both sides.
Anyways, I respect your analysis so hopefully we can get some fruitful discussion on this
Again i'm not claiming += i'm just claiming =. Not that I couldn't be wrong, but I certainly don't think it is as easy as you claim. I actually think black's best chances lie in 1. e4 c5 2. b4 axb4 3. a3 e6 4. axb4 Bxb4 5. c3 Be7 6. d4 Nf6 where the position starts to take an Evans Gambit feel to it. However, I have seen 3.... Qa5 to great effect though the positions often seem to have a French Wing Gambit appeal here.
I would also be perfectly willing to play some correspondence games with you for fun (or bragging) in thematic style of pairs (one white, one black, two white, two black etc) of any starting position you choose (though not until January too busy over the holidays in case my responses be come slow this is also why).
Cheers.