Some noise from the transformer is normal, but usually not very much. The first thing would be to check the mains voltage setting. If set for to low a voltage, it can hum loud but also burn after some time.
Also a partially broken rectifier (one diode open) could cause extra hum. Another cause might be excess filter capacitance (e.g someone changing the filter caps to larger values).
Changing to a switched mode supply is not a good idea. It will add extra noise, unless you get a really special low noise one. Especially common mode signals are a really pain to get rid of.
Adding rubber buffers ans sometimes extra glue could help against to much hum.