Yeah, I have the exact same bass, ESP vintage 4.
I also changed the P-pickup to SPB-1 vintage. I really liked the SPB-2 together with the bridge pickup, but alone it was too "muffled" on the high-end and I dont think precision basses need any more middle on their sound
Now I am really happy with the sound! You should keep the SJB-2 bridge pickup, It works great with SPB-1!