Its easier to put out the match before the forest fire. If the transformer is an EI type and has feet, it can be isomerically mounted. That does a lot more than damping a chassis that includes a transformer with mechanical vibration.. Vibrations from transformers can get into tubes.
You need a slightly larger hole for the bolts mounting the transformer, in which isomeric grommets are placed (EAR makes excellent examples; if DIY on a budget you use rubber grommets). A fender washer is then used on either side of the grommet and then the bolt goes through the whole thing secured by a locknut (so it won't come off even though its not tightened down much). Now there is no metal in contact with the chassis and so vibration is vastly reduced. You may find that a lot of the mechanical noise from the chassis is simply gone- that you have to have your ear very close to the transformer to hear anything at all.