Mechanical hum is from vibration in the coils and possibly the laminates of the transformer. The only way to resolve that really is potting the transformer. That is, dipping it in something liquid that will harden once cool/dry and lock all the wrappings in place.
On guitar pickups we pot them in a wax bath, as the vibrations translate to high pitched squealing by the time it gets to the amplifier. But those are low voltage and pretty much zero heat devices. Knowing that pickups will...well, pickup the noise and send it down the line, I'm betting vibrations in a power transformer sends distortions on down the line.
Transformers can be ordered potted, but since our Triplite stuff is for general use, not hospitals or recording studios, they don't care about the humming transformers.
The Triplite I picked up is a hospital grade one, so it's much quieter. They must use a better transformer in it.
Typically potting compounds are epoxy or resins. It needs to be a pretty thin viscosity to really get into the coils and laminates. It helps if it's thermally conductive so you aren't encapsulating your transformer in an epoxy blanket. LOL
http://www.digikey.com/product-search/en?Cat=1179754&k=potting%20compoundhttp://www.mouser.com/Search/Refine.aspx?Keyword=potting+compoundI hope that helps some. I have a transformer I'm thinking about doing this to...I'm just too busy/lazy to get around it to.