Just a bit more information for the group: the pot I bought is a 32 QT 4mm NSF Aluminum Black Label 1100 Alloy commercial stock pot by Johnson Rose (Product 6542 -- I would link it directly but they go out of their way to prevent that for some reason.) This may sound silly, but is there a chance the pot is "defective?" Can you really have a "defective" aluminum pot?
I don't see how this could be a "defective" pot, but maybe the fact that it's aluminum is part of the problem. When I started brewing with extract, I used a 5 gallon stainless steel pot with the "tri-clad" bottom (like the MegaPot). I could boil 4 gallons with the pot on a single 2500 watt coil - due to the stove configuration I couldn't straddle two coils. It took a long time to get to boil, and it wasn't a vigorous boil, maybe just barely boiling, but it was boiling even with the lid off. Maybe the difference is due to the fact that stainless steel doesn't conduct heat nearly as well as aluminum? If that is the case, then some good insulation might work for you - the trick is to find something that won't melt or catch fire.
One thing I did notice was that after running that one coil at max for a couple of hours, the entire top of my stove got awfully hot, so maybe you would be better off in the long run with a heat stick to help your stove - I bet even a 1500 watt heat stick added to the stove power would do the job.
EDIT: The coil I was using was 2500 watt, not 1400.