It's a shot in the dark trying to give a meaningful suggestion if I can't see what you're doing, but since no one has responded yet, I'll throw one out and hope it helps you in some way.
Pulling wire through a length of tubing is always going to be easier than pushing. So if you're able to rig your wires to a string or something that threads through your sleeve so can pull the string at one end of the sleeve and feed your wires at the other end, hopefully you can work your wires through easier than squeeze/push if the sleeve in question is not able to, I guess, dilate.
I've had to do stuff like this dozens of times for much simpler signal applications i.e. other than audio, so while I think I'm describing a great idea, you might have some nuances to work your way around. Like breaking your conductors.
Do you think perhaps you need different sleeving, perhaps something with more give, more inner diameter? Does your sleeve cooperate more when you work it a bit? Random but relevant things to think about.
I studied a cable mod I found online where the modder taped up his wires to a bullet nose shape so they travel better through the tubing.
Wow, this post has, like, zero flow.