Sarah; Reversing polarity is not necessarily the same as being out of phase. You may be reversing polarity of the AC power, much like reversing the AC plug. This is not changing the phase of the output to the amp. I am not familiar with BAT preamps to know if that switch reverses the phase to the amplifier or just the AC polarity. You should consult with BAT on that (check the manual). Reversing the AC polarity to the wrong polarity will usually make it brighter as you describe.
Preamp makers make their preamps out of phase (going out the amp outputs) usually because less is more. Their designs are simple and clean (and out of phase), and would require an additional gain stage to bring them back in phase. The addition of another gain stage would degrade the signal.
Conrad Johnson preamps are out of phase. You could call them or drop by on your way around the beltway and have them explain it better than I can. They are behind the Home Depot at Route 50 and Route 29 in Fairfax.
Sometimes CDs are recorded with the polarity reversed (by mistake), but reversing wires won't help. It needs to be corrected at the DAC. Some CD players have a switch on the remote to reverse the polarity for these CDs.