I have just watched your video. Have you measured the width of the backing plate at various positions?
This could indicate whether the previous owner faced it in order to make it run a little truer.
(although it could have been faced both sides)
If you tighten every thing up, and clock up a morse taper using your compound slide,
re-boring the spindle should be do-able, A reamer would probably not be the best option anyway
as it may clean-up the high spots but be pulled out of alignment by the existing run-out.
Re-bore and then ream,if the spindle is not too hard, would be a dream solution.
good luck.
Melv.