The 1 st test game (in progress):
2. e4 King's Head Nf6 Reversed Damiano 3. Nc3 Bc5 4. Na4 Be7 5. c4 d6 6. d4 exd4 7. Qxd4 Nc6 8. Qd2 O-O 9. Ne2 Nd7 10. Nec3 Bh4+ 11. g3 Bf6 12. b3 a6 13. Bg2 b5 14. Nb2 Nc5 15. O-O Rb8 16. Kh1 Nb4 17. cxb5 axb5 18. Ne2 Nc6 19. Qc2 Be6 20. Bd2 Re8 21. Rfd1 g6 22. Bc3 Bxc3 23. Qxc3 b4 24. Qd2 h5 25. Nf4 (+0.00) ½-½
All right, black had the constant advantage that increased in the beginning (almost till ev =-1) then diminished till the strict 0. It means that white suffered but had enough ressources to rebalance the situation during the middlegame. 
Preliminary conclusion: Barnes opening is bad but non-refutable.
The Barnes opening 1. f3 is probably the worst 1st move. I wonder whether it can be wholly refuted at the level of strong engines. [Damn, it would refute the wonderful Hammerschlag 1. f3 e5 2. Kf2 too
]. I'll start with 2 test games (Explorer vs Explorer, d=20):