Bottom line up front: If you are looking for a P sound and get an SR4, you will still be looking for a P sound.
If you are looking for a P sound, get the P. If you want to add more sonic choices, an SR4HH is worth an audition.
I think the scooped Ray tone gives a good fundamental, and the transient attack comes through in the mix because of the strong treble content. The Jazz with both pickups on full kind of has this also, a scooped mid, but because of its active pre, an SR can really boost the treble, I think more than 12db. I don't particularly like the Ray sound by itself when I practice, usually have to roll the treble back. But is just sounds right when set flat when playing with others. Mine is an SR4H, not an SR4HH.
Also, I find that a lot of the P bounce comes from where I pluck it. I sit on the pickup. The Ray pickup is closer to the bridge, so I get more high harmonic content. Kindo like the diff between plucking on the neck and bridge pickup on the Jazz.
Only my humble opinion.
Bruce