I think the nose protector should push the collet holder out the the spindle when you unscrew it.
I use a rod through the spindle from the rear and a few bumps and the collect adapter should pop right out.
My Hendey has a collet adapter in an L style head. It cannot be pushed out from behind because its through hole is larger than the through hole in the headstock. I have a forked wedge that slides into the gap and a light tap pops it free. Much like a ball joint or tie rod splitting tool. OK thats my two cents.