Bluzdog & Ian - exact same thought I had. Just checked back into the forum after a couple of days and here's where I am.
Made a bounce of the kick track with a gate, high pass @ 134, big boost @ 1261.9 - gotta love digital

- and a compressor to bring out the punch of the attack.
AS still leads the transient by what looks like a fair bit on some of the hits. That said, when I used the resulting MIDI track to trigger Session Drummer, I no longer hear double beats. Totally usable. Problem Solved.
In fact, I'll probably never use audio snap for this purpose again with out doing this. The gate alone has saved a ton of time weeding out errant snare hits etc.
Thanks for all the help!