After much adieu over nothing I suppose (since at the moment I only have
one to do) I decided to turn a tapered mandrel between centers. The
first one turned out pretty good except I screwed up the finish pass(es)
and came in under sized. No I can't just shorten it up. So I still
have just one to do. LOL.

I picked up one of those little offsettable centers and it worked well
enough, except the tip melted. I kept it lubricated, but it might have
just been to high of an rpm for the method. I can turn it slower, but
if I get to do more of these I sure don't want to go slower.

I have two thoughts:

I can offset the tail stock and use a ball bearing center.

I can machine off the melted center, center drill it, and insert a ball
bearing between it and the center drill on that end of the stock. The
ball bearing certainly won't melt, and it will more evenly distribute
the load from the stock to the center. It would also have more contact
with the drilled out center. It would also allow me to have a small
reservoir of grease behind the bearing.

I really don't have a strong feeling for which approach will work out
better other than I dislike the time spent adjusting my tailstock back
in. I can leave the offset center setup for this taper indefinitely.
Ok, maybe I hope the ball bearing method will work out atleast as well.

The taper is pretty shallow. .157 over 10 inches.