Well, I figured the faster I got on it, the more likely I could maybe beat the full curing process of any recently applied adhesive.
I got out my trusty $5 needle files. Used the triangle shaped one to cut grooves at the "quarters" inside the broken tenon piece within the stummel.
I then used the thinnest flat tool from the Leatherman to gently pry the "quarters" away from the briar wall.
I had just finished steaming some veggies for dinner (thanks, bluto, for mentioning heat) so I stood the stummel in a glass in the steamer after the heat was just turned off for about 5 minutes.
Dried the condensation off, snagged an edge of the broken piece with the needle nose Leatherman jaws and out she came!
Now, I just need to find someone to replace the tenon in the stem, right?