I have seen people use an old muffler on the air intake to help noise. CMU block walls, and a fire proof steel door seem to work well too. if you like spending money. That plus, inner walls with insulation and some Quietrock, you'll never hear it.
I dont know how well it would work in this application, but butyl rubber roofing under layment like grace ice and water shield is very similar to dynomat. I think it works best on surfaces that resonate, like steel panels though.
Ideally you want to add density to your wall, to slow the transmission of sound waves, but you also want to isolate components so that vibrations can not transfer through them, making noise on the other side.
If your framing a wall, you might consider using 2x6's for the top and bottom plates, with 2x4's for the studs. Put them 2' on center, on each side of the 2x6 so that they are staggered every foot down the length of the 2x6. you can then weave something like the butyl rubber between the studs. This also allows for more insulation. By staggering the studs, sound will not travel through them, and out the other side of the wall.
For a door, if your looking to save money, you could try using more than one. In the same frame, have one door that opens in and one out, like a door between hotel rooms. A bit ghetto, but might do the trick.
As far as egg crate foam, and carpet, its my understanding that it does little to actually dampen the sound transmission. What it does is reduce echo inside the compartment, making it sound quieter. Its cheap enough that it cant hurt though
Just a few thoughts.
Lightfoot