Might have this concept wrong so bear with me.
What about scrapping the chuck, fit a collet chuck and just nip it on the work.
Push the work thru the collet with a pneumatic cylinder or even lever feed, stop on the LH outboard end so you feed the same every time.
Drill in a block on the cross slide.
Part off tool in another bock.
Write a program to start spindle, position drill and drill, retract, move to part off, feed new length, wash and rinse.

Basically you have re-invented the sliding head lathe.