Thanks 'extropic', I appreciate all the Likes you gave. FWIW, many years ago, I had more Likes than posts but back in 2012 or 2013, we got hit with destructive virus and my post count and Likes got erased.
Answer #1: To check the shaft, I coated it with bluing and used the long edge of a HSS tool blank to scrape the high spots. I checked the tool blank on a grade A table and verified it to be flat. The taper technique is also shown in this build thread:
https://www.hobby-machinist.com/threads/bull-nose-live-center.64859/
Answer #2: The motor... I called the distributor and they recommended a test to let it run for a while. They were willing to accept a return if it was not satisfactory after break-in. I decided to let it run in 30 minute intervals for 4 or 5 hours. The heat problem resolved itself and is due to the fresh rubber oil seals breaking in. The vibration also smoothed out to an acceptable level but, I'm still planning to take it apart to see if I can balance the rotor a little better.
Gratuitous BS: FYI: The project is still on hold until while my shop is being reorganized. I need to build a table for that grinder and I'm not inclined to do welding until the weather improves where I can do it outside. Also, the metal frame/box needs to be sandblasted and painted -which I don't do until the garage is opened up.
Ray