How to get rid of transformer hum?

Fpeel, this is a different problem than yours. This does not sound like a ground problem but it sounds like the culprit is power line harmonics. The chopped off top of the sine wave suggests that something looking similar to a squarewave is feeding the device. A squarewave's spectral makeup is the sum of all of the odd harmonics. If you looked at the power line on a spectrum analyzer you would probably see lots of odd harmonics. I believe it is these harmonics that are making the transformer laminations loosen and vibrate.

Tommy, I apoligize for my over simplified explaination but have you thought of something like the PS audio box that recreates or regenerates the sine wave? Another possibility is a used ac power source. I have seen some manufactured by Elgar at some of the used test equipment houses for about $1.5K to $2K. Good luck.