I have a Fender Squier sixties classic vibe precision bass and I have it in the tuning of BEAD. When I first tuned it down with the original strings there was obviously a lot of rattle so I got Rotosound drop zone strings going up to .135. The thicker strings makes it a lot tighter to play but I was recording with it earlier this month and I noticed a problem.
The tone of it is quite bad. Sounds a dull bell. I thought maybe this was a problem with it being recorded direct in but I recorded with my friend's really cheap and rubbish bass and it sounded a lot better.
I have tuned a number of basses to BEAD over the years with mixed results. I have the most success with active basses and basses with Jazz pickups. P-bass type pickups never gave me any good amount of focus for a low B, just boom. The Squier P pickup just might not work well tone wise for a low B. I have also needed to raise the pickups really close to the B on order for it to sound balanced at all. Good luck!