Peculiar. I am guessing one of three events is going on:
1) the former owner made a deliberate modification to keep the drawbar from sliding out of the spindle. Hence the split gear cover.
2) the closer is somehow inadvertantly jammed onto the spindle, and the split cover was an unrelated modification.
3) former owner was unhappy about the collet closer setup wobbling around in use (they do tend to do that a bit) and fitted some kind of sleeve to tighten up the fit.
I think the best approach right now, short of using a knock-out bar from the right side, is to attempt to image what's going on inside the upper part of the gear cover. (of course, try the soft mallet on a collet threaded into the drawbar, lightly, first) How is the upper cover fixed so it does not fall down on top of the collet closer? There should be a single pin protruding from the smooth part of the spindle (outboard of the drive gear on the spindle) that the *slot* on the collet closer slides over. You can see the slot in out of your former photos, where end of the slot is visible outside the gear cover. If you look in there you should see the pin.
It's possible there's been a screw or other attachment mechanism put in instead of just that pin.
If the drawbar can rotate slightly (slack between pin on spindle and slot) that means it's set up properly. If there is zero rotational slack that means something else is going on. You say the drawbar can move laterally a small amount - about how far does it move right to left before it hangs up, and does it hang up hard when it stops?