I've been taking a page from Mike Mahoney's book and using a piece of 3/4 inch MDF, mounting it on a face plate and turning a groove in it to match the size of my bowl (tight fit to hold it). I then just push the bowl into groove I cut and bring the tail stock up to make sure it's good while I clean up most of the bottom. I move the tail stock out of the way once I'm ready for removing the final nub on the bottom. The sanding is done with the bowl mounted this way as well, minus tail stock of course. To get the bowl out of the groove, I just tap the MDF on the back side and it pops right out.
All that being said, the donut chuck looks like a nice way to go. May have to see about making one of those.