Mumetal is good for small external fields. It's common in the old CRT based oscilloscopes to wrap the CRT with a cone of mumetal to reduce beam wiggle from external fields. See
https://en.wikipedia.org/wiki/Mu-metal
Magnetic fields are very difficult to shield. There is no such thing as a magnetic field "insulator" like there is for electrical fields. The "resistance" of free space to magnetic fields is too low. Ferromagnetic materials can provide some shielding because they have an even higher "conductivity" for magnetic fields than free space. The ratio of how much better they are at conducting magnetic fields than free space is termed their "permeability", and normal transformer iron can be up to maybe 10k to 20k times better than free space.
Mumetal has a permeability of 80K to 100K if everything is just right, so it can be much better than even transformer iron. If everything is right, that is. When any ferromagnetic material saturates, its permeability drops to the same as free space, so ferromagnetic materials are only good up to some maximum magnetic field. Above that field intensity, they may as well be cardboard. Mumetal has a very high permeability, but also extra low saturation density. So it goes free space on you at low field intensities. But that is enough in some instances.
Conductors can also shield a CHANGING magnetic field. Non-static M-fields cause eddy currents and other field effects in conductor sheets, and this either eats the energy in the M-field as heat or diverts it with field effects. The Faraday cage construction uses field effects to shunt changing fields around the outside of the cage.
Highly effective magnetic shielding uses both ferromagnetic and conductive layers to increase their effectiveness. Good mike input transformers may have a four or five layer shield of mumetal/copper/mumetal/copper/mumetal/copper... to do this.
If a sheet of mu-metal does good, that's great. It's quite expensive, as you found. Check your scissors, though. Mumetal is notoriously hard on cutting tools, as it work-hardens just ahead of the shearing zone. And as you may have found out, it cuts hands like a razor blade, especially in thin sheets.
I would be very interested in seeing how different your results are with a box of 0.080" soft aluminum sheet around your OT is from the mu-metal. I've always wanted to see this, but never would pony up the money for mumetal. That's not just cheapness - it used to only be available in $100 minimum orders, so having it available in an 8x12 sheet for $40 is new to me. It's a great opportunity to test the theories in the real world.
In shielding, you try to shield the source of the noise first, then shield the target. In this case, it would be useless I think to put mu-metal around the PT or choke, as the fields are big there. Putting thicker aluminum or even sheet steel around the noise sources would cut the radiated hum somewhat. Mumetal should be reserved for low-intensity areas, like the OT. It's probably most useful on PP OTs, as I suspect that the "DC" leakage field around an SE OT might saturate it.
"It's not what we don't know that gets us in trouble. It's what we know for sure that just ain't so"
Mark Twain