In the SEX amp, the plate choke and output transformer do interfere with each other to some extent. They are however carrying the same signal, so any mutual pickup is not easy to notice or measure. But a power transformer carries only hum, so it would naturally induce that into the signal-carrying plate choke.
Toroids have quite a different field from E/I laminations, so you can't count on substituting one for the other keeping the same magnetic orientation. For the same reason, you can't simply apply the flux ring (copper shield) concept without figuring out the magnetic fields involved - and making sure you don't create a shorted turn inside the loop!
Our own power transformers are designed with a low magnetic induction, whereas commercial units usually have the maximum magnetic induction possible. The reason is that this has a powerful effect on size and cost.
Magnetic shielding also requires some knowledge of magnetic properties. For example, plain steel has a permeability for small signals that is much much smaller than mu-metal. I can't quote a number but it's on the order of 100 times. So for the same shielding effectiveness the steel would have to be 100 times as thick. At high field strength though, mumetal will saturate and loose its shielding effectiveness long before this happens to steel.
You could for example get an external 240:120v transformer to power the system, using 240-v primary transformers running at 120v. Just a thought.