AmpegInsider, your test results are different from anything I've ever experienced. Maybe that particular amp does something that sucks power when it clips? I don't know. Were you measuring actual RMS current? Most amps present an overall resistive load (albeit not wholly resistive, and not linear, either) to the AC line and do not compensate for low mains voltage by drawing more current.
The most efficient operating point for an amplifier is right at maximum power--right at the threshold of clipping. That's where (Power out)/(AC Power in) is at its highest. That's fine for peaks, but in music, most of the time the signal level is well below max, so the vast majority of the time, the amp is operating at very low efficiency.
That's why design engineers came up with amp concepts like class G and class H, in which the amp has essentially two or more maximum power points, shifting automatically between the lower and higher powers automatically.
Lowering the mains voltage makes the supply rails sag in about the same proportion, but it doesn't change the amp's gain in its region of linear operation. This lowers headroom but brings the maximum power point closer to the signal's average power level. The ratio of (Power out)/(AC power in) increases, so the efficiency of the amp itself goes up. This may sound like a benefit, but losing headroom is overall a bad thing. The efficiency of the overall system has not improved, because when the mains voltage drops, it's because more power than normal is being lost in the wiring and distribution.
To the original question, I would meter the AC outlet without a load. If it's not up around 120V, ±5%, to begin with, you're already starting at a disadvantage. You can't fully test the AC outlet without a load, either, and as Nightbass pointed out, if you want to see how the outlet holds up with a 1000-watt load, you'll need something that will dissipate that much power, such as a lamp (like you've been using already}, a big resistor, etc.
If there is a relatively large amount of resistance in the mains wiring, the voltage will drop significantly under such a load. Check other outlets. Sometimes it's poor wiring to or a bad connection at a single outlet. This is potentially dangerous; whenever I find a faulty outlet, I tape over it to discourage its use and notify someone in charge of the venue that they should get it fixed.
Another tip: whenever you use an extension cord, it should be as short as possible and as large a wire gauge as practical. In addition to the 100-foot extension cords, I would suggest maybe one or two 25-foot cords.