The best option is to find a way to keep both.
The next best option for me would be to keep the Stingray and buy a used Squier Matt Freeman that is basically a Classic Vibe 70's bass that looks just like your Pbass. Great basses that sound, construction, playability , and feel far out weight the price tag.
They are hard to come by used but check Reverb, Guitar Center Used , Craigslist, MusicGoRound daily and post a want to buy ad here. You should find one .
Or as other option is keep the Stingray and buy a used USA Peavy Fury. If you like a Jazz style neck and great P bass tone, you might like this bass. But the Freeman will get you that same Fender Vibe and feel of a true Precision bass neck and tone.
There is one on Reverb right now. FYI they don't last long and people seem to hold on to them. Im not the seller . Just offering assistance.
Like you, I adore the Pbass tone. I feel it is something that everyone should have in their arsenal. My limit is 2 basses. Instead of going with an American P, I chose a Squier Classic Vibe because well lets face it, it really doesn't require a lot of money or to be USA made to get great vintage Pbass tones, build, and playability . Am I saying my CV Precision is as good as a USA made Fender ? Nope. But I am saying it gets me close enough to where I'm not unhappy or feeling like Im missing something .
When it came obtaining more modern tones that a Bass cant deliver, thats when I found it necessary to spend the money and by USA. So I went with Ernie Ball MusicMan Caprice.
Those 2 basses do everything that I need them to do. If you feel the need and your budget increases later on, go buy another USA Precision . They aren't that hard to come by. It would be harder to replace that Stingray .