I agree with you Lee about the bandaid. What is TBC?
I'm using the live center that came with my Shop Fox mini lathe and the MT1 mandrel from PSI. It's probably a combination of things, this whole process was bad. I didn't drill it straight and had barely enough material on one side to even cover the bushing, but I figured since it was going to my everyday pen I could make it work. Then I tried to rush it, then tried to disassemble it and totally wrecked it.
TBC - Turning Between Centers. Use a Dead drive center for the head stock and a live center for the tail stock.
You basically told me your problem: You use the live center that came with your lathe, and it was made for wood, not metal as in the mandrel. The mandrel has a little dimple in the end (60° dimple) and it requires a 60° live center. The wood live center is not 60° and it wallows around in the dimple just enough to cause your problem.
IF you continue to use the mandrel, you will need a 60° live center. They are available from several places.
Grizzly, WoodCraft, PSI, JohnnyCNC, LittleMachineshop.com, Amazon and others have them. IS the ShopFox a 2MT (Morse Taper)? I am fairly sure yours is - anyway, you want to make sure that you get a 2MT 60° live center. But if yours is a 1MT, you will need a 1MT 60° live center.
Back to TBC. Turning between centers is a method that is much simpler than using a mandrel. Much less parts. It consists of a Dead (non-live) center in the head stock and the live center on Tail stock. Put the bushings into the squared blank and put that between the two centers. Tighten and turn. Once the blank is close to size, remove the bushings and put the blank back on without the bushings. Measure with calipers for sizing. Finish. Measure finish with calipers too. Perfect finish sizing! No mandrel flex from chisel pressure; No mandrel flex from tail stock being too tight; no bent mandrel problems. No bushings stuck (glued) to the blank. No chipped blanks from separating the bushings after finishing with CA.
Some people don't like this as they prefer to finish both blanks together, which can only be done on a mandrel. That is fine. 90% of the people that use TBC after having used mandrels stay with TBC. It just eliminates lots of problems that are associated with mandrels.