Funnily enough, after years of searching for "the one" I am starting to realise that I had it and sold it.
I currently have machines of almost every description, headless, 4's, 5's, spikey shaped Deans, fretless this and that, but the one that is nearest perfection IMO is a Dean Edge that I bought off eBay for £36.00. Not a P I know, but passive and uncomplicated.
I think it may well be time to close the loop and return to the Fender Precision that I started with.