First, thank you all for the feedback.
The humming sound comes from the fan-side of the lamphouse, and not from the transformers, of that I am sure. The fan purrs, while this humming sound is distinct. The humming happens with or without the voltage stabiliser. Something I did not clarify: the fan cable is not plugged into the voltage stabiliser. We plug the lamp cable into the back of the voltage stabiliser's output socket (which has a power rating of 600 VA). The voltage stabiliser and timer are two separate units but are wired together (the timer does not have its own socket). We did some tests on another enlarger, a Varioscop, which only has one plug (and no fan), and operation appears normal, no fuse popping.
On this enlarger, there is one cable with socket for the lamp that gets plugged into the timer and another plug for the fan that goes through two transformers. Something I did notice is that, when jiggling (or moving) the fan cable with "homemade" switch, the fan motor proper begins to make a strange, high-pitched noise but then will stop once you "crimp" the cable "back in place" -- this suggests some kind of faulty connection and I hope to get to the bottom of it this weekend.
Another issue is: we have not yet grounded our electrical installation. We will do so this weekend. Not sure if this has any bearing on it or not.
Anyway, I will get our electrician friend to put a meter on the cables and hopefully we can get to the bottom of this.
Thanks again for your help.