Considering your budget, I'd look for one of these two on the used market. Classic '50s (MIM) or an American Special.
Both have killer P-Bass tone. My Classic '50s was my "go-to" for years, even though I have/had other great, more expensive basses. Just a great value. As mentioned though, these have the wide nut width (1.75").
This American Special was offered awhile back. I absolutely love this bass. Excellent tone, and the neck is one of the nicest, easiest-playing necks ever put on a P-Bass IMO. The nut width is closer to what you're used to (1.625" as opposed to the 1.75" width on the '50s Classic). If you can find one of these used, jump on it. I'll never get rid of mine!
It did come stock with the parchment guard, but I put the gold anodized on it and like it much better. Here's how it looks with the parchment:
Both have killer P-Bass tone. My Classic '50s was my "go-to" for years, even though I have/had other great, more expensive basses. Just a great value. As mentioned though, these have the wide nut width (1.75").
This American Special was offered awhile back. I absolutely love this bass. Excellent tone, and the neck is one of the nicest, easiest-playing necks ever put on a P-Bass IMO. The nut width is closer to what you're used to (1.625" as opposed to the 1.75" width on the '50s Classic). If you can find one of these used, jump on it. I'll never get rid of mine!
It did come stock with the parchment guard, but I put the gold anodized on it and like it much better. Here's how it looks with the parchment: