... Also, get a long straight edge and see if the LS is bent. A machine crash can bend a LS.
I don't really think pumpkin head gravity is bending the LS. A shaft that diameter and length will not bend visibly in the middle when supported at both ends. Disengage the HN, turn the machine on and see if it wobbles. If so, it's bent. Best you can do is try to straighten it.
Could also could be extremely worn-out bearings at the supporting ends. In some cases, there's no bearing at the TS end and the LS is just stuffed in a hole. The hole could be way oversized. Drill it out and make a bushing.
Ray