irving, the sticky out-y corners will be permanent because they form a series of halving joints, if you cut them off the thing would fall to pieces.

I don't know what you plan to line the shed with but I found celotex (50mm thick) from the local builders merchant to be good, it's a thermal insulation but it can also attenuate noise. Because it's quite soft you would need thin plywood over the top, thickness appropriate to what you want to hang off it. Of course this reduces the inside of the shed by over 100mm each way.