[hazmail]

Red - As you say, keep it simple, that feed problem can be solved with a sliding collar (with another bearing !!!),on the square stock, and a bar hooked up to the carriage for the cutting head. As the head returns to start another run, it drags the timber through the chuck and onto the dead center. As the head starts cutting the collar slides back up the timber, ready to lock on and drag another length in.
This collar would be set up on a cantilever system similar to a 'Hi Lift' jack (without all the switches and pins etc). A more simple use of this cantilever principle (what you need), is the one way locking mechanism in a 'Mastic gun' or sliding 'G' clamps.
Saying all this, I never got this far, but that was what I was going to try and use - centering after it comes through the chuck may be a problem (use guides maybe), especially if the stock timber is not strait .pete