Advice on a single coil for a Quarter pound P/J bass build?

Hey all,

I recently decided that I wanted to turn my project P Bass into a P/J and I am looking for some advice on which single coil pickup to choose.

The project bass is an old Candy Apple Red Squier that I got cheap off of a friend. I replaced the original split coil pickup with a Seymour Duncan SBP-3 split coil, but what type of single coil should I place in the J position? Would it be more worth it to buy a new pair entirely? I got a good deal on the SBP-3 so I am not opposed to that either.

Alder Body and a replacement Jazz bass neck in rosewood as well (The old neck had bowed and broken beyond repair, which is why I got it cheap. Shhhhh I don't have poopie polishing syndrome, I just like to tinker.)

Thanks