I need to cut up a 6" HDPE tube with square ends. So I'm thinking of
mounting it on my lathe with cones to center the tube and keep the cuts
square.

The problem is I can see how to turn a cone (or at least truncated cones
for this large of piece) that will mount to the headstock but not sure
how to keep a cone straight when held in place on the tailstock. Yes I
know the pressure will hold it in place but this tube is 36" long and I
can see problems trying to keep the whole mess in alingment while trying
to tighten the tailstock.

I'm thinking of drilling several inches into "face" of the cone with the
Jacobs chuck while the cone is still unfinished and still mounted to the
headstock. Then when I mount that cone on the tailstock run a steel rod
through the tailstock in hopes that would help stabilize the alignment.
The rod OD would have to be the same as the tailstock tunnel's ID to
reduce the slop.

Anybody had experience using large cones to center tubes?