I took the advice of
@paul darwin but since it was out-of-warranty, I sent it to True Sound in California as recommended by Rega's US distributor.
I was contacted by True Sound today, and he seems to be extremely knowledgeable, and explained that the high hum level is normal for the Aria Mk3, at least in the US, and has found the same level of hum in all the Aria's that have passed through his bench. He explained that the transformer coil was more designed for the UK, and in the US generates more EMI which is then picked up by the other circuits. He does offer some modifications at a reasonable price which he's done on other Aria's to greatly reduce the hum, which I'm considering having done - or just sticking with the Fono MC as it doesn't have the issue, with the transformer being outside the chassis.
I'm still somewhat baffled why there have been mixed reports of hum with the Aria; maybe owners without the issue are in the UK, or maybe some people are less sensitive to the noise.
P.S. He also mentioned the Brio has the same issue, since both have a large transformer coil in a similar half-width chassis. Googling "Brio Hum", indeed it seems to be a common complaint.