So now my question is, how much damage have you caused to the Morse tapered sockets on your lathe in the name of aligning things? I can't think of any instances where the headstock and tailstock are (or need to be) rigidly coupled during turning. When you are spindle turning, the connections to both ends of the wood act as flexible couplings in which there is very little angular displacement. The end result will not be any different between perfectly aligned centers and those that are off by even as much as 1/16 inch. What will, however, cause a problem is when the point of the center at either end inscribes a small circle rather than running perfectly true. And, I suspect that use of the double-ended tapered insert could eventually become the root cause for a spindle socket that doesn't run true.