Nathan,
A picture nail does mar the walls, as you say, but I figure any good painter can make it disappear with spackle (when the time comes). I never had a landlord who objected to normal picture-hanging holes. There probably are some, though.
Picture nails (the kind with an angled disc at about 60 degrees to the nail) seem to hold better than plain brads, but still, drywall is a horrible substance on many counts. If you've ever lived in a house with old walls of plaster, horsehair, and wood lath, you know how much quieter such rooms are. The construction soaks up sound like a sponge, and the uneven thickness of the plaster (much thicker than drywall) prevents resonances. But drywall is a lot cheaper to put up, and that's progress.
You had some other interesting ideas. As to free-standing panels, I have some of the stretcher-mounted foam leaning against the walls in a couple of places, and they work well. I do think there's probably an advantage to having the back of the foam uncovered, rather than mounted to a rigid sheet, but I'm no acoustician....
...Mike