Hum on a choke loaded stage

[Sandor]

The tube output stage of my DAC produces a very audible hum.
It uses stage a single E88CC (one half for each channel) and anode is loaded by a 140H choke.
I have found that rotating the two chokes (90 degrees for the right channel and 45 degrees for the left channel) the hum vanishes. A buzz remains, but only audible at a very high volume level. Taking the chokes off of the box, the buzz vanishes too.
I have also found that hum and buzz get louder putting the chokes closer to the transformer and to the choke of the anode PSU.

1) Is there any shielding technique that allows a quiet output not dependent on the position of the chokes?

2) Can I solve the problem enclosing the anode PSU in an aluminium box or mounting an aluminium separation between the chokes and the PSU?

Best regards.

Paul