good wishes from a distance to you and your family.
Here's a page from StewMac, showing a pre-wired P-Bass harness, keeping soldering to
a minimum. They also sell the components, so you can save dollars by soldering it together
yourself. I've done this and it's not difficult. And I've also used the pre soldered kits, which
work great. Your choice. StewMac sells the proper components for your bass, which means
250K pots.
http://www.stewmac.com/Pickups_and_.../Golden_Age_Pre-wired_Harness_for_P-Bass.html
I shielded inside the pickup cavity and inside the control cavity on my "rescue" P-Bass, and assembled the
new wiring myself, and it's dead quiet. I used Nashua Tape from the hardware store, which isn't as fancy
as the expensive copper shielding you see sold by Luthier suppliers. But my luthier recommended it and
it does the same shielding for a fraction of the cost.
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My P-Bass was made by Squier in 1997, and was abandoned by its owner in the basement of my brother's wife's business. It lay down there, buried under a bunch of forgotten things for an unknown number of years, until found by the guys cleaning the basement. She gave it to me in very bad condition, and I took it on as a project
after my luthier got the neck straight. I named her Raven and she can take her place onstage next to instruments costing thousands, and not give up a thing.
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By comparison, yours is in much better shape! I agree with others here that the de-oxit may solve all your problems and your bass may be playable with no mods other than that, which would be a blessing.
The Precision Bass is the original, designed to do
one thing very well. But these days, with the amps
and pedals we get to play through, the simplicity of the P-Bass design is no handicap. Mine has a world
of tones available, and does more than one thing. But I like to keep it simple anyway.