… but the MIDI timing output by major DAW programs is very inconsistent.  Hard to believe, but most DAW clocks are more unreliable & jittery than some of the drummers I’ve worked with.  And that’s saying something …

It’s been quite a while since I’d tested Ableton Live against some others, but my conclusion was to go with an outside MIDI Clock in hardware.  When I use Cakewalk Sonar (or similar) live, I sync it as a slave to a Lexicon MPX 1, or even to an ancient Yamaha RX-21 drum machine as the master clock.  I split the MIDI clock to software and hardware in parallel routings.

It’ll be difficult to determine where your CC message problems originate without more specific information or examples.  The clips themselves (saved to .mid) would allow for testing by someone else here. Or at least a detailed listing.  You don’t want to send too many MIDI messages to the H9 in quick succession.  Is your H9 set to its own MIDI Channel (or Omni)? 

That #3 point sounds like two ‘high’ CC values are being sent out one after the other.  What CC values are you using as the ‘triggers’?  In other words, are the CC values in the range of 64-127, with no CC values between 0-63?