That's the nature of the beast IMO. I'd swap it for something else. Like a PAF type, lower on output that the misleading name implies with more hi end. Just my 2 cents. I'm partial to SD Custom 5's or even JB's for more output. Personally I like the A5 mag pu's in LP and LP type guitars.
I put one in the neck of my carvin califonia carve top with a gibson iommi in the bridge. I kept the three way but removed the push pull split and disconnected the tone pot. Straightforward but killer tones! I love it for everything from funk to metal. Try it in the neck with something else a bit warmer in the bridge, I think you will be very impressed.