The Randall Isolation looks like a great idea. The only problem I see in this case is that it's basically a single speaker closed back cabinet with an isolation box attached to the front. This is going to sound quite different than a dual speaker open back Twin. The walk-in closet idea mentioned before seems like the best kind of solution - though it's better to line the closet walls with insulation rather than cover the amp.
If you want to build a dedicated box, a simple plywood box lined with acoustic foam will give quite a lot of sound isolation. "Black Hole 5" insulation is even better, but it's very expensive
http://www.speakercity.com/damping.shtml). I can also explain how to make something similar for a lot less money if you're interested. You want to make the box about 1 foot bigger than the amp in each dimension (about 30"x36"x24" HxWxD). This will give enough volume so you don't alter the speaker properties and also allow unrestricted airflow between the front and back of the amp cabinet. When you put the amp in the box, place it slightly off center and a bit diagonal. This will help reduce standing waves and avoid a "boxy" sound.
Caution: The biggest risk here is heat. You will essentially be creating a little tube amp oven. You could potentially damage your amp, or even worse cause a
Fire .
This danger makes everything more complicated. I would highly recommend either building an external mount for the amp head (with a shield like the amp cabinet has) or buying dedicated speakers and building a mock cabinet that goes inside the isolation box. The latter would give you the convenience of the Randall, avoid the hassle of disassembling your amp, but still retain that Twin open back sound.
Anyhow, a multi purpose isolation BOOTH like a closet would be the best overall solution.
barefoot
