I've had this problem on a couple of P basses.In my case the string was misaligned ( badly fitted bridge,thanks Fender..) which lead to the E string being directly over one of the pole pieces instead of between them.If this is the problem,you can get saddles with sideways adjustment to realign the string,or do what I did which is replace the pickup with bar magnet pickups (no pole pieces) such as EMG's.The passive version is cheap and didn't noticably affect the sound.Or you could try a lighter guage E string.Also,rather than raising the other pickup,have you tried lowering the one under the E string?