Just an update for future searchers...
I was able to unlatch the seat back from inside the trunk without too much trouble using a flat blade screw driver. Then, since I couldn't get the pull-up handle and housing out of the top of the seat, I left it in the seat top and simply drilled a small hole in the pull handle and threaded a long zip tie through the hole and down to the latch mechanism leaving the head of the zip tie at the top (it can't get through the small hole and acts like the head of a fastener.
It took 5 or 10 minutes of fiddling with screw drivers, needle nose pliers, etc., to get the tongue end of the zip tie to thread into the hole to which the original pull cord resided on the latch mechanism. Once that was threaded through the latch hole, I pulled the zip tie all the way down tight (such that the pull-up latch at the top of the seat back was down in its well) and took the heads off of a couple of other zip ties and used them to cinch up the zip tie nice and tight to the latch mechanism.
That's it. Now when I pull up on the release latch, the catch opens just like new. No slop and nice and firm. Should out last me!