Ok, here's what you need! @bassman_feb_64 will also want to read this too. Sorry Alan I meant to be in touch!
You're best option is to source a Fender non-export CIJ PB70-70US BK. This was actually a limited edition colour of the usual olympic white PB70 (US) available from Fender Japan. The non-export models have a few things about them that makes them better in my opinion too. The bass is black and may come with a mirror scratch guard (very Phil Lynott) but I have seen the odd version that comes with black. Possibly an after market upgrade. Mine I had to source the correct 70's scratch guard.
These basses come with chrome hardware, John Deacon's upgrades (that came with his black respray around 1985) includes a Schaller 3D bridge and very likely Schaller tuning keys, though I much prefer Gotoh's FB30 (Or the Wilkinson equivalent) simply because I find the longer key shafts more appealing on a 70's P - think pre '76 nickel tuners and you'll know what I am talking about.
Bass Player Magazine did a whole thing on John Deacon that I helped write, if it helps.
Funnily, the Nate Mendel is an option as it's the next best thing, but the PB70-US is just a far better bass, I only wish it came with an Ash body. - On the subject of Ash body, if you wanted to capture John Deacon's early years, then I'd recommend the Fender non-export PB70-70US Ash RW which came with a sunburst finish, as his two precision basses were, stock (the TV script version and the silver spaghetti logo bass)
For my own basses, I am lucky enough to have a natural 76 Precision, which is just delicious and my next Deacon build is going to be a black version. I think this will be number 4, I can't remember! I sold my first black P to a lovely chap here on BassChat and miss it dearly! Such is life and bills eh!