I can't claim direct knowledge off this, as i'm not really an electric player, but i'd be surprised if anything you built along the lines of movable panels made any difference at all in what the neighbors heard. Isolation like that requires tight (ideally airtight) construction and a lot of absorbent material, etc. considering that they are already hearing the sound through walls, a couple panels on stands aren't going to substantially cut out any more sound. (Unless there's currently little to no isolation; e.g. no walls or only incredibly flimsy walls between you and your neighbors...)
Again, AFAIK. Someone correct me if you'd had success with this, but typically neighbor issues are dealt with by adding drywall to walls, adding wall insulation, dropped ceilings, and the like. I.e. not easy. The classic low-budget technique where a club throws some blankets on the walls to try to keep the neighbors happy is a well-documented waste of time.
Not that it's a bad idea to make the panels for recording, though.
Edit: ninja's by Bristol; and yeah, if you share a floor with your neighbors, get the amp off the floor with some foam or whatever.
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