I guess I was not terribly clear when I was asking for information on gluing down the leather. I have not had a problem with a grip moving after being sewn on since my first bow 12 years ago, not one of the subsequent 100-something bows.
For this bow, I wanted a one piece grip with a tab that extends up along the fadeout on the side of the bow such that it would provide a softened arrow pass. Since that tab extends up above where the rest of the handle lies, it cannot be sewn down to anything, and must be glued down to the side of the bow at the fade out.
Here's the grip and the leather pad glued to the fadeout from my first bow:
I used Duco cement back in the day and every 2nd or 3rd time shooting the bow I would have it half falling off. So I'd grab it like a Band-Aid, give it a rip, scrape off the glue and re-glue it down. As you can see, there isn't a thing you could do to "sew" that tab without it flapping in the breeze. It must be glued down.
For the record, the leather on my "inconvenient takedown" was wetted, stretched, sewn and allowed to dry overnight. No glue on the grip and it was going NOWHERE. I used TBIII as Pappy suggested, careful to wipe up any excess squeeze-out with a soft damp cloth. For a dozen shots, like I said, it was a certified shooter! However when she failed, I decided to test the glue up of the arrow pass tab. TBIII bonds well enough between spar urathane and leather that I will certainly use it in the future.
I am now gluing scraps of leather to the remaining shards of bow limbs to test the other suggestions.