I'm going to give you a strong push in the direction of the U-turn
I advise against fixing your current turntable. It is over complicated and could cost a fortune to fix, if it is even possible. In addition it is an automatic turntable and therefore designed most likely from someone who wandered in from the bicycle industry. The stylus just needs to move the lowest friction bearing possible in the base of the arm, not gratuitous junk. Lastly it is Far Eastern in origin, and personally I don't think they have ever designed, or produced a really good turntable, except possible for some lunatic scratch DJs!
Although I have no experience with the U-Turns,their design looks excellent andhas all the right attributes. The first of which is simplicity coupled with good engineering.
It is designed and built in America. That is the one I would pick.
Despite the last years huge advantages and progress, I still derive a lot of pleasure spinning my legacy disc collection on my legacy turntables. So since you have the old "software," I say go ahead and take the plunge.