I am going to urge, persist on the notion that the wiring at least be inspected and troubleshot. Most of the other solutions require pulling the pump out anyway, the wire has to come with.
I do not comprehend the use of single conductor wire down the well string. I am not an installer and therefore not a professional well installer, therefore I am not familiar with the practice of deep well installations. However, I would personally not opt for such cabling. I would deem multi-strand cable to be better all around. Physical strength, decreased line loss due to skin effects, hysteresis and current eddies, physical flexibility and overall ease of application or use (handling).
Maybe that is the norm in the water well field, which I am not well versed in, but in my specific line of work I understand other parameters which are also important. Very short runs of solid conductor wire are beneficial. Long runs with high AC current are not beneficial or are less so for several reasons.
Gordy (RADAR)