These are all good things to check and could be contributing factors. Put a dial indicator from the cross slide top surface to the top of the threading tool, and observe the readings while cutting threads. That will give you some indication of the rigidity of your setup.
Based on your water-glass videos, it does not appear to me to be single-phase motor induced harmonics. When those issues have come up, the videos make it crystal clear that the motor harmonics are at issue, and I do not see that in your videos. What I do see is probably belt thrashing or out-of-balance pulleys on the motor or on the headstock end where the belt attaches. Have you observed the belt-thrashing behavior while threading? I replaced both pulleys with balanced high-quality version, and the OEM belt with a notched Gates Tri-Power belt on my 1340 and was rewarded with better surface finishes.
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But the kind of surfaces you are getting while threading suggest more severe fluctuations at the cutter-to-part interface. This could be rigidity issues stemming from the relatively
weak mounting T-nuts for the compound on this lathe, or it could be some other loose gib in the compound or cross slide, or a loose tool post. An indicator from the cross slide to the top of the tool doing the cutting will tell a story.