There's a dimple on this one because I didn't use the Tail Stock Steady to turn out the recess on the bottom. On the Mesquite Bowl I was able to hold it with a Cole Jaw and turn out the bottom, but I see the dimple now so I guess I used the tail stock live center as well.
Kevin, since you have Cole Jaws also, mount your piece in them, then bring up the live center to take the tenon down to at least a 5/8" nub. Remove the live center and insert the Tail Stock Steady. Bring it up until you have the right pressure. You don't need a lot. I usually grab a tire, and rotate it back and forth a couple times. If it slips, tighten an additional 1/4 turn. Look at the flat you create on the tires. It should look similar to what the properly inflated tires on your vehicle look like. If you tighten them too tight, I guarantee you will have a blowout.
Turn on the lathe, and start from the nub end, and cut towards the headstock. Keep cutting from the center working towards the headstock until you reach the bottom. Repeat until you have completely removed the tenon remnant. If you were to start at the bottom and cut straight in towards the center of the nub, you could possibly have too much pressure on the tool and have the nub break off, inadvertently leaving small tearout that you can't get out. It would look like those dimples you have in the bottoms, but irregular.
What I do is start at the center of the nub as described above. I keep working it until I reach the bottom, leaving a sloping nipple. Go back up and start cutting again. I suppose that would be called down hill cutting. I keep checking the height of the nipple until it's below the foot. When I get the clearance needed, I usually cut in several rings, using Easywoods diamond tool. If the foot is tall enough, or I'm doing a pedestal form, I'll make a finial.
My motto is, If the bowl bottom doesn't look as good as the bowl, you ain't done. Decorating the bottom is as important as turning a good looking form. I don't make flat bottoms anymore, and I don't leave any inside 90 degree corners anymore that could reveal a recess mounting, which I never use.
I'm not trying to hijack your thread. Just trying to help since you have the best bottom cleaning tool out there. ........ Jerry (in Tucson)