Fender Precision - with Jazz neck?

[Rusco]

American P Bass Special (not the deluxe one) is exactly this. They're not currently in production but you occasionally see then second hand. 

I have a sunburst one and they're worth trying out if you can find one. Cheaper than the equivalent American Standard P of the same time period. I think they were the Highway One evolution. 

[Quilly]

If I was going to do a swap Id have a J body with a P neck !  

The chunkier the better 😅