Last month I bought a fine cut No. 3 Morse Taper to do exactly what you described for the skimming out the tailstock. I have been waiting for an opportunity to change out my 4-jaw chuck so I can insert a MT5 dead center into the headstock for accurately centering the reamer. I normally use a 3-jaw chuck but lately a lot of my projects require offset turning with the 4-jaw.
Thanks for confirming the technique.