I don't think the cover is significantly acting as a speaker cone, because if it were, gripping it tightly with my hands should dampen its vibrations and reduce or eliminate the humming, but doing that doesn't affect the sound of the humming at all.
I tried putting a sheet of thin plastic folded to match the shape of the cover (a transparency sheet for inkjet printers) between the cover and the base as an insulator/separator, but it made no difference at all. I also listened with just the clear plastic being used as a makeshift cover while holding it tight against the bottom sides of the base, and even that produced hum, though quieter than the hum you get with the steel cover.
I think that just enclosing it with anything is creating a resonance chamber or something to that effect.
I also tried putting rubber washers under the transformer's feet, as well as under the heads of the two mounting screws (4 rubber washers in total), which completely isolated the transformer from direct metal-to-metal contact with the housing, but that didn't make any difference at all.
Putting rubber on top of the transformer (as suggested by BrokenYugo) that's thick enough to press against the cover does quiet the hum by a noticeable amount (no cover at all is still quieter though). I'm guessing that the metal housing of the transformer is the primary "speaker cone" here, but it doesn't make any noticeable sound unless it's in a small, enclosed space. Rubber being pressed against the top of the transformer would dampen its vibrations some.