I have a manual approach which works for me at least.
That's pretty much what I usually do too. I made some bars (think t-handle without the T) to fit my chuck so it's easier to turn.
I also made a spring loaded centering too for the tail stock so I don't have to advance it as the die or tap cuts.
What is keeping the die centered on your setup? I don't see anything between the die and the quill.
I cheat. I put hex die in 6 jaw chuck (3 jaw would work as well) and put the stock in the collet chuck. make the collet chuck proper torque. When putting in the hex die either rest on chuck face or use parallels to make sure it is not off in your chuck.
Sorry Tom, I cannot visualize your process at all. Sounds like you are using a collet chuck and a 6 jaw simultaneously??