We're all guessing here ATM, but it does look as if the AD600BM is down on expected brightness and it's certainly true that the flash tube sits much further back into the mount than it should, kind of firing out of a tunnel. FWIW, my thinking is that the mount is blocking some of the light, but also in a double-diffuser softbox a lot of light is bounced straight back towards the flash tube where it gets tangled up and absorbed by the mechanism and lost down the tunnel, IYSWIM.
Perhaps along the same lines, when you fire a speedlight into a double-diffuser softbox, extending the zoom head setting not only increases the hotspot, but also actually reduces brightness. Guessing again, but maybe there's something similar going on there.