That is kind of helpful.
Next is to rig up a monitor, and Compare what is different about Logic’s clock and Ableton’s clock.

I would theorise that Ableton is sending some extra signal that interacts with the Harp Algo in some way… And Logic has a more ‘clean’ clock. Should be determinable on a monitor. Alternatively, the Harp Algo ~requires~ some dumb extra signal that only Logic provides.
This case also would benefit by direct comparison of the signals.

Either way, this sounds frustrating.

Side note… Do you have ANY other MIDI assignments on the H9? It might be helpful to unassign any parameter adjustments or hotswitch assignments… Make sure that the H9 at least nominally should only be responding to clock. Maybe that’s where the crosstalk is?