You can put in a large isolation transformer and create your own neutral. It is called a "separately derived system" in the NEC handbook. I designed a 50 KVA split phase line system, 120V-0V-120V, from 3 phase 208VAC using two 25KVA isolation transformers for a solar energy lab here in CA. This is the basic 120V/240V mains in North America. You will also need a suitable earth ground on the output neutral. For your system, a 10 to 12KVA isolation transformer will do, such as a Square D or equivalent. Do get a good one, the cheaper ones have very little headroom.
The hum in my I have found in my system deals with the transformer magnetic field driving into the chassis and creating a leakage current flowing to the earth ground wire or through the RCA shields. I don't recommend isolating your equipment from earth but you can isolate your transformers in your equipment from the chassis using grommets. To test this theory, remove all connecting cables and plug the unit into the mains, then turn it on, and see if you have hum. If the unit does not hum and if it does not have a earth ground in the power cord, connect the chassis to earth and see if it starts to hum. If it does, you have found part of your problem. Do this for each piece of equipment that plugs into the wall.
Also, I did have one obscure hum problem once but it was the receptacle where line and neutral were swapped. I had hum every time I plugged something into this outlet. Given what you published, I assume this is not your problem. You can get a outlet wire checker at your local hardware store for 10 bucks or less - it will save you from opening up each outlet to check the wiring.
The hum in my I have found in my system deals with the transformer magnetic field driving into the chassis and creating a leakage current flowing to the earth ground wire or through the RCA shields. I don't recommend isolating your equipment from earth but you can isolate your transformers in your equipment from the chassis using grommets. To test this theory, remove all connecting cables and plug the unit into the mains, then turn it on, and see if you have hum. If the unit does not hum and if it does not have a earth ground in the power cord, connect the chassis to earth and see if it starts to hum. If it does, you have found part of your problem. Do this for each piece of equipment that plugs into the wall.
Also, I did have one obscure hum problem once but it was the receptacle where line and neutral were swapped. I had hum every time I plugged something into this outlet. Given what you published, I assume this is not your problem. You can get a outlet wire checker at your local hardware store for 10 bucks or less - it will save you from opening up each outlet to check the wiring.