Similar to Paul, I finish the recess in advance, fancy it a tad if I think I want it that way, and let it alone. Few beyond other turners will care if the bottom's jazzed, because to see it their guests would have to spill the beer nuts.
Only weak spot in this method is wet and warp stuff, where you will have to sand the bottom to sit flat as a minimum, and leave it a bit oval after drying. I can live with it, but if it's not your thing, be sure to leave a witness mark for center and use it to snug the disk or vacuum chuck you're using to hold it to refinish. When I use it, I do a tapered disk and hot glue. Then I have to decide if I want to blend the new bottom with sandpaper or not. Makes leaving it oval my favorite method.