If the rail coil is indeed a Hot Rails, then you really can't juice the output any more, and you need to reduce the mids in order to get it to sound more Stratty. May be easier and better to fix this in your signal chain rather than at the pickup. Boost with gain on your amp or use a pedal, add brightness in the same way, reduce mids in the same way.
I also think that the goals of hotter output at the pickup and more "strattiness" are not complimentary goals. Hotter output typically means woolier fat mids and reduced highs, while Strattiness to me means sparkly highs and less mids. For classic single coil sound that isn't weak, I've had much more success running classic single coils into a boost pedal. Gets the extra punch without changing the fundamental sound. You may even LOWER the pickup, which can clean up and open up the sound, and then boost it with a pedal before your amp.
Another option since you aren't using the functionality of the P Rails is to swap for a regular 'ol Strat pickup.