Pulsr actually just answered this question in the post before yours. I've been playing the May/A.B.A. matchup and it's even worse that he describes. ABA out-ranges May, out-prioritizes May, out-damages May (barely), and has a reasonable answer for anything May can do. The ONLY saving grace is that May is decently equipped to make her hit the floor three times, but even this is offset by the fact that ABA can now switch herself out and then back into Mohora with one combo.
So yeah, just learn ABA and that should help you take care of May. It also has the added bonus side-effect of being good against Jam as well. Still won't take care of that pesky Eddie problem, though.