Sounds like you need to have a look at your mids. The neck pickup is collecting a tone that has far fewer mids than the bridge pickup will produce. Try boosting them on the amp first.
If that doesn't work try any EQ pedal with mid controls, maybe with a sweepable mid frequency. You could look at the nifty little EWS BMC (bass mid control). Very simple tiny pedal with sweepable mid frequency and boost/cut control.