Track mute with long samples- how to make them come straight

Apologies if this has been asked before, but after searching the forums I couldn't quite find an answer for my specific situation...

So, I've recorded a bunch of beats in Ableton and I'm now going to be performing live, where I hope to use the MPC 1000 as the only bit of kit (I'll also be doing some vocals over the top).

My plan was to export each track in Ableton as an individual file, assign them each to a track on the MPC, then play the sequence as a loop and mute and unmute tracks to provide variety. The problem is when I mute a track and then unmute it, because it's only triggered at the start of the sequence the sound doesn't play again until it reaches that point. I'd like to be able to bring sounds in and out mid-loop, on the fly. Is this possible? Or is this set-up not the right way to do this?

Sorry for the slightly convoluted explanation! Thanks in advance for any help.

here are 2 solutions:

Chop it up
chop it into 16 or more pieces, and just record the sequence playing those in a row. That might work, since I would guess your mutings/unmutings would happen to the beat, depending on the length of the sample, chop it into more samples if you want finer control.

Better solution:
Get JJOS and use audio tracks. The audio tracks will mute/unmute and resume wherever it should be in the sequence. The free version of JJOS might do, it allows for 4 audio tracks. (unfortunately they're set to tracks 61-64).
Even better, get one of the paid versions of JJOS, you'll get more flexibility with audio tracks, as well as tons of improvements overall.

Thanks for your help. I'll have a mess around with the free version of JJOS and see how that works and/or try chopping it up, as you're right, I'd be muting/unmuting on the beat. It's a bit of extra work, but not insurmountable!