Since you only have a single 20A outlet, you could use a single Furman 20IS with a power strip.
You are correct in that you only have 4 high current outputs. These use the series mode noise and surge protection, but not the balanced voltage conversion.
However, your problem is going to be total output power. A single 20A outlet cannot provide more than 2400 Watts of power at any given point in time. Having said this, you may not need more. 2,400 watts is a lot of output.
Your best option is to get as simple a power strip as you can, without built in surge or noise protection, and use them to increase the available outlets.
You know what you may like, Parts Connection makes these 6 outlet extension boxes as kits, with built in V meters. This will help because if your HT ever causes your voltage to sag, you'll see it.
I would also get ferrite beads, they will help reduce any switching noise which leaks from the amps. They are super cheap. Once you have built the strips, you can snap them right on.
Alternatively, you could use a Furman conditioner with the same filtration, but only the high output sockets:
This has 8 outlets built in, but lacks the power factor correction:
If you absolutely must have the power factor correction: