I googled and it seems that people are checking the spindle with dial indicators. I have one which I recently bought, but I don't have a holder. Since the dial indicator does not need much force to hold it in place, I just put it on top of a few boxes and blocks and it worked fine.
It is off. So I marked it, took it off the headstock, and whacked it with a hammer. After a few tries, I have finally get it close enough, and on it goes.
Here is the test cut after straightening the spindle. On the left was the best I can get before rebuilding, and on the right is with the newly straighten spindle. It really looks much better.
The advantage of having a weak spindle is that it can be corrected really easily if needed.