To increase your options, if it doesn't have to be Precision shaped, although still sounding like a precision, it is worth considering a Hondo II Professional H1015 - the double cutaway job. Necks are brilliant, sometimes they have DiMarzio pickups. Bridges are generally crap 3 point jobs. Weigh a ton but that might not be an issue for you. Sometimes they can be picked up for peanuts.
Also a Westone Thunder, although prices for these have rocketed recently. The 1A, particularly, sounds huge.
If you were really lucky an early Peavey Fury might come along. They can be usually picked up for very little and are a quality USA built bass. 'The best precision bass Fender didn't make' I have seen written. V. slim neck, aggressive pickup with a superb tone.