If you hear a buzz instead of a hum the problem may be induced noise instead of a ground loop. Try turning all the other circuits in your home off as a quick experiment. It could also be a result of the amplifier transformers being too close to your other gear.
You don’t want to ground 2 prong devices. The lack of grounding is keeping them from being part of the problem, nor do you want to use a cheater plut.
First issue is to narrow down your problem. Disconnect all inputs from your processor, and put it and all your amps on the same Furman conditioner. See if the hum still occurs. Then start turning amps off.
Despite the fire department recommendation, you CAN extend a Furman conditioner with a pure power strip that has a built in breaker, like the one below. The reason fire safety people are concerned about daisy chaining power strips is that many strips and power cords are not fused and easily overloaded. The unit I show you below is 100% safe to extend a Furman power conditioner. Just don’t use a cheap, unfused/unprotected power cable in the middle.