If all else has failed, try new pickups.Yes, with both pickups, it scoops a lot. The best situation I've found is to solo the neck pickup and the bass becomes "useable" but still not where I want to be.
I have two Rays, one with rounds and another with flats, both cut through with no problem. I even have a Squier VM Jazz with 15 year old flats that comes through better than this Fender Standard with new rounds.
I cannot understand this at all..