Is there any benefit in adding an aluminium shield in my phonostage?

I know this is an older thread but think it's worth mentioning ----

Regarding shielding against magnetic fields, at 60 Hz aluminum's skin depth is about 10mm -- close to half an inch. That's pretty thick. In contrast, mu-metal's skin depth is about 76 microns -- .076mm. The difference is mostly due to mu-metal's much higher relative permeabiility. It's a pretty stark difference and shows why mu-metal is often used where EMI due to magnetic fields is an issue.

Mu-metal isn't a panacea for all situations where mag-fields are involved. Its Bmax, the field at which it saturates, is very low compared to mild steel. Above Bsat its mag-shielding properties are pretty much gone. It still would be OK for electric fields, though.

I used an online skin depth calculator to obtain the info above. The skin depth for mu-metal may not be exact because I used Nickel's resistivity, but because mu-metal's relative permeability is around 50,000 I don't think minor variations in the resistivity will matter much.
 
An update.

The hum is definitely caused by the mains.
I installed a Power Inspired AG1500 in my system, and the issue is no longer there.
The new transformer has been installed, and it will be connected to the mains network in the next two weeks.

I am looking forward to having a better quality power supply.