Pots are very simple components, they ought to have a negligible effect on tone provided that they are an appropriate value for the circuit and are not scratchy. You can change to a different value tone pot for a different range of tones but one is not ‘better’ than another.
Really glad to hear you are digging the bass after a bit of time with it. The behaviour of the pots where they seem to have most of the control in a small part of their throw (especially in reference to the interaction between the two volumes) is 100% normal for a passive jazz bass circuit - my ‘74 is exactly the same and so was my old VM jazz. It’s to do with the cancellation that happens when the two pickups are at the same volume pot position - when that cancellation comes in, it does so quite suddenly.
If the pot is still scratchy, you could try just turning it from 0-10 back and forth for a while. It sounds simple but it often works for me, I live in a high humidity environment and often find that my pots are ever so slightly scratchy if they haven’t been turned for a while (the scratchy sound is caused by a fine layer of oxidisation on the contact surface of the pot). Turning it a few times wipes it clean. Whatever you do, don’t use a ‘pot cleaner’ spray - they’re more likely to ruin pots than fix them.
If the body is 6.6lb then that is phenomenally light for a jazz! That indicates that the body on your particular bass is very light, and that would be the cause of the neck dive. Lighter tuners and a heavier bridge might help, but if the body is that light then it still might dive even still.
The headstock blemish is I think pretty reasonable given the price of the instrument.
Re the looseness of the pickups - do they just need their screws adjusted so that the pickup is snug?
