Those tapered spindles are common for quick-change buffing and fine scratch (wire) wheels. I would be hesitant to use them with heavier grinding wheels. Nice job on the wood base. That's what I would have done with a hardwood like birch or maple. Cherry is also quite hard.
Does it vibrate about the same with nothing attached? If so, are the bearings sleeve or ball/roller? Can they be replaced? Armatures can be balanced, but I have never tried doing that.