He just does, Jeff.

Stan Potts uses one too. (They may not be Carter Just Cuzs, but they're exact in form and function. I actually think Lee's IS a Carter.)
Shoot Rick James a PM and ask him which one he hunts with; he's posted pics of it before, and I can't recall the model... but it's a thumb-trigger like you're talking about with the crisp sear break like you're looking for but with a cord tying it to a wrist strap.
So basically... someone's already thought of what you're thinking of.
I remember the first time it happened to me in archery... I took a Cranford EZ step, cut off the threads, hada machine shop weld a plate onto that at a 90-degree angle, and then attached my bear quiver holder to that so I could screw it into the tree trunk beside me at waist level. Just when I was thinking of getting my idea patented, I discovered that Kwikee Kwiver had been making their caddies for a long time... [8D]