I got an Allparts neck (one piece maple) for a 51 style Pbass recently. I'm very pleased with the quality, has correct construction (walnut stripe, square heel, cross head truss rod in the right place) and fretting is great - no levelling needed. I also got a good discount, so its always worth calling for advice and having a chat.
I've also had good quality necks from WD music in the past. Brandoni are worth a call - they may have good NOS fender style necks, but can't display them due to Fender licensing issues.
Generally you can expect to do some minor work on the tuner holes to get a good fit, and maybe some slight fret levelling. But fitting the nut well makes the biggest difference to overall playability.
The hard bit is the nitro finish - I'd get the body and headstock face sprayed professionally and oil the back of the neck. Most of the replacement bodies are polyester and you can tell the difference, however well done.