If the supply voltage drops at the breaker, I would guess first that the problem is with the supply, and that the extra load is bringing the problem to the surface. It's probably either the PoCos problem, or you have a bad connection on your side.
Try tightening all lugs on your mains coming into the panel, and everywhere else that you can get to. Make sure all the busses are in good condition and that your breakers are seated properly and the contacts are all in good condition.
If that does nothing, call in your PoCo to check their connections at the x-fer and behind the meter (if you can't get behind the meter yourself because they have it locked out). ALWAYS BE THERE WHEN THEY COME OUT so you can show them the problem UNDER LOAD, or they will not see the problem at all.
I see this problem a lot pretty often,and it's usually a loose connection or a bad main feeder.
Please let us know what you find, and good luck!