Audio Noise from my step up/down transformer

DO you hear it the same with any source switched to on the integrated, for example phono (if present) versus aux or CD?

See if physically moving the transformer further or closer to the integrated causes a change in the noise level at a particular volume.

If so, relocating it further away from the integrated might help.

If moving it further away seems to help but you can't move it far enough away, consider options to add some additional magnetic shielding around the transformer for better isolation.

You probably have a power imbalance and you are using too small of a transformer for the task. This causes transformer core saturation on either the positive or the negative AC cycles... leading to harmonic distortion and a DC offset that induces noisy ground loops which are easily picked up on RCA interconnects.

Your amp uses something like 240 Watts when run at 220 volts suggesting it will need around 500 watts at 110... so I would use at least a 1000 watt transformer to be on the safe side.

P = I X E

P = power, watts, va
I = amps
E = voltage

P is the same on both sides of the xfmr.

I would agree more than likely the problem is caused by a ground loop.

Jetrexpro,
I can only assume the step-up transformer is an autotransformer.
Could easily be checked with a continuity test.

Unplug the xfmr from the 120V power....

The neutral blade on the 120V plug will have a common continuity with the 240V neutral contact of the 240V receptacle.
At the 240V receptacle, there should not be any continuity between the safety ground contact, of the recept, and the neutral contact of the receptacle.

A temporary test using a ground cheater could be used on the 120V plug of the xfmr just to check for sure the problem is indeed a ground loop hum problem. (Only perform this test if the xfmr is an autotransformer.)