BE wouldn't have changed the outcome of the match. We might have won 1-2 games, but I doubt we would've won the match regardless. If it was a full stall deck, then yeah, BE was a game winning card, but not with so much damage from them.
Assuming BE in place of either purify or CS, and assuming same draws:
g1, he locked me down other than EE for most of the game, and hid his hand for the last several turns
g2, he drew both purify and CS early, would have been close
g3, he had one squid against three recluses for several turns before I drew SW
With BE, I'm probably losing this match after three games if I haven't lost already