This may be worth doing if you know how to rewire the power transformer for 240V operation. The power transformers in equipment made for both 120 and 240V markets often have two primary windings; the two primary windings are wired in parallel for 120 V use and in series for 240 V. If that's the case, it's an easy mod, but you'd better be DARN SURE you know which lead is which!
I'd say it may help because:
I was able to dim the meter lamps with heavy bass passages ( which is a second output winding on the transformer for the lamps ) which started me thinking about this.... So I ungraded from a 14gauge 10 foot extension to a 12gauge 10 foot extension... this improved the sound and reduced the dimming some....
those lamps dimming means something is causing a significant voltage drop. Can you run it without any extension cord and see if that is contributing to the problem? If that is really a 2.2 KVA tranny I doubt it's saturation, although that could be an issue.
If the load you're putting on the house wiring, power cord, etc. is causing a significant voltage drop, then setting it up to use double the voltage should help by a factor of four, not two, because the voltage drop will be half, and, since the primary is stepped down by a factor of two more, that voltage drop of half as much is reduced by another factor of two.
To illustrate:
To make the math easy, say the output of the transformer is supposed to be 90V with an input of exactly 120 or 240V, depending on how it's wired, and the input power is 1200W. Say that all the wiring from pole to transformer primary has a resistance of 0.2Ω, and the return side of the circuit is another 0.2Ω (that's a lot, but makes the math easy and illustrates the point).
It's drawing exactly 10 Amps at 120 V (that's 1200 Watts); the wire resistance of 0.2 Ω on the hot side causes a drop of 2V. The resistance on the return (neutral) side costs another 2V, so the voltage at the transformer primary is 120 - 2 - 2, or 116V, a 3.3% drop. The 4:3 transformer reduces 120V to 90V, so 116V at the primary produces 87V in the secondary.
Now, if we rewire the PT to double the length of the primary winding, and double the voltage, it will now draw 5 Amps (5A X 240V is still 1200W). 5A through .2 Ω is a 1V drop. Another Volt is lost in the other half, so the voltage at the primary is now 240 - 1 - 1 = 238V, (a 0.83% drop, half the previous drop from a higher starting point). It's now an 8:3 Transformer, (240 in gives 90 out), so 238 in gives 89.25 Volts at the secondary.
In the example, you've lost 0.75 V instead of 3V.
Give it a try and report back, please.
[edit] Nikola Tesla, "the man who invented the twentieth century", was THE MAN!