Marty, looks like you're getting there.....

Yes, transformers do hum on their own, especially old larger ones.

The laminations can come loose over time, and if it's a metal/rattly hum then you need to get the tranny re-dipped in laquer to seal it.
Otherwise you just need to work on resting your tranny on some form of isolating bed.

The silicon is probably still a bit too firm, and therefore transferring the hum from Tranny to cabinet.
Also to note, you might wanna mount the tranny on 4 rubber standoff posts, this way you get the main bulk of the tranny off the cabinet, and there's only 4 points of contact via the posts, although they should be rubber anyway, and absorb hum too.
Placing a foam/pillow block under the tranny can help support it and dampen the hum around the posts too.

Other options are to perhaps mount the tranny on it's own small wooden base (to keep it secure) and then mount the wooden base on the foam/rubber standoffs.....even 'spring' standoffs are an option.

In an ideal world, you would actually replace the BIG tranny with several smaller ones, they hum less (being smaller)
this will also isolate your power rails and stop current drain on 1 supply from flickering (dimming) the other one(s). but that's another avenue....

MM.