Tough one without replacing the entire door with something considerably more substantial. Maybe sliding glass or at least the same door in a solid core format?? If not, you might consider filling the door cavity with low expansion foam to at least deaden some HF leakage, though this will do precious little from around 2-3 kHz on down. If anything, make the gaps around all sides of the door (and frame) as well sealed as possible. Good luck - and I think the reason more of us don't have this problem is that we have dedicated areas (or rooms) for our gear that makes this problem moot.
-Richard
-Richard