Well if you are getting more signal at higher freqs then you are getting more wattage... If you are getting less signal at lower freqs then you are getting less wattage, so yes that could defiantly and sounds to be the problem.....
Because the more volume (SPL) you want the more the cone has to move, larger voltage potential. So, if it's crossed over at lets say HPF 60 Hz, above 60 will move the cone more than below 60 because it is getting more signal...
It doesn't sound like an amp problem, because that wouldn't affect the frequency if the amps bunk it's totally bunk not just higher up unless it was in the active circuitry which controls the crossover in the amp. The box wouldn't make it do that either, because if you were playing below tuning the speaker would for sure bottom out, it's not the speaker because a speaker isn't frequency sensitive (it is but not this much), it's not the coil out of phase because then you would have maybe a half inch movement. If it's moving the cone a lot at higher frequencies it isn't the level from your head unit, because if it was it wouldn't move it a lot at all....
So, that leaves one problem.... Crossovers, or that your headunit isn't outputting the low frequency.... Unless I'm leaving something out....
SO, run out of the Sub-out not the non-faded out, check all connections from the head unit to the speaker... Make sure you are running the RCA's in the IN on the amp not he out or bridge..... And with out setting there looking at it that's all i have.....