I think the Korg PA80 and PA1x will play one shot samples as well as play samples across the keys, but not sure if there is an auto loop feature. I've had the PA80 for almost five years now and have never used the sampling feature. You can use custom voices in the styles, so this sounds like it should be possible. I'd recommend posing the question at the Irish Acts forum. Lot's of avid Korg arranger users there.
I can do the same with FL studio and Orion Platinum as you with Ableton live. I use my laptop with one man band and I think it would be fairly straightforward to send a midi output from OMB to FL or Orion ( or in your case Live ) using Midi Thruway. I can send the Midi output of the PA80 into the laptop as well, so I know that would work without a hitch. I already have done this at times to get better voices for drums, bass lines etc. It send midi clock data from the styles, so no problem syncing up.
AJ
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AJ