how can I make a large transformer less loud?

The sound is a result of the system creating large magnetic fields as a function of how it operates. These fields are fluctuating, probably at 50Hz based on your input voltage but maybe 60Hz if your in the US.

These magnetic fields push and pull on components in the system, since perfect dampening isn't possible these components vibrate. Some of what you hear isn't at 50/60Hz though, it is also harmonics of that frequency and interactions with other components.

You definitely shouldn't do anything that will limit air flow or otherwise create a situation where the transformer could overheat.

You can poke around a bit (carefully) and see if you can find a particular components or panel that is vibrating and try to use something to dampen the vibration. High Temp Dampening material may be an option.

That being said, transformers of that power are basically impossible to silence. The transformer core or the windings are probably vibrating and causing most of the noise. At high enough power levels the iron core itself actually stretches and contracts as well causing vibration.

Some designs try to isolate the core to prevent vibrations transferring to other components but its not something you can likely fix in an after-market fashion.

The explanation I've usually heard is 'loose laminations'; at least one of the laminations has room to vibrate with the time-varying magnetic field.

Not sure what can be done about it. Some transformers have bolts through them to hold the laminations together, and it might be that tightening them would mitigate the buzzing somewhat. If there's an obvious gap somewhere, there might be some way to get some epoxy or something into the gap that would limit the freedom of movement of the adjacent laminations.

You might not be able to do much about the noise directly but you can always redirect the noise such that you hear less of it.

Lower frequency noises are more difficult to absorb, they tend to travel right through the material. Thus wrapping a towel around it won't do much. They are however easily reflected by a dense hard material.

Build a sturdy sound wall around one side and that should redirect the noise somewhere else while keeping good airflow to the transformer.