Most of this discussion seems to be how to reattach the cut sheath to keep it from separating later. Make it easy on yourselves... get a speedo shop to make a cable 18 3/4" long and slip it into the housing. Done. Forever.

 

Found this while researching the issue this morning. Seems like the best solution to date.

 

FINISHED!

I just completed both sides. From the time I posted this last post and this one I did both headrests. No heatshrink. I did just like this chap showed, except I put a dab of gorilla glue in each end before I pinched it just for good measure. I would have been done a lot sooner if I had figured out that bottom upholstery fitting sooner. When I got to the second side I laid bottom piece flat against the board and the folded the upper seatback piece under and it just snapped into place super easy. I think it took 2 hours total; getting tools, doing the work, putting tools away and then vacuuming up the dried up crusty old foam bits.

I think this fix is a done deal and won't have to be done again.

 

Just a note of thanks to all the contributors to this thread!
i just completed the repair of my pax seat which was demonstrating the "runaway motor with no headrest movement" issue. I used the "cut off the cable ferrule, drill out the remnant sheath material, re-insert the sheath" method, and it works a treat.
Of interest is that reinserting the sheath can be facilitated by gently heating the raw sheath end with a heat gun. That will soften the plastic enough to ease the insertion.