Chris, I mentioned the Hafele hardware in the first post. Never tried it, so let me know if my understanding of what it does is wrong.
And now for the really simple solution!
1. Run the door on edge through the tablesaw, cutting a kerf through the center of the stile to within 1/16" of the panel groove.
2. Cut a kerf-sized bit of material to fill the resulting slot.
3. Spring the door into the opposite twist, and glue the stile back together along with the new center laminate.
Postscript:
I did this on both doors on the hinge stile, springing the door opposite to the same extent of the original twist. One came out perfect, the other no change. I did the second one again, this time with double opposite twist. Perfectly flat.
So, I assume that on the first one I was working on the stile that was exerting force, and on the second I was working on the opposite stile. Anyway, all good, and no finish work on either face. A simple solution that doesn't necessitate purchasing some spendy bit of hardware... Even though I was really hoping to sell you all a bunch of those springy things. Thanks all.