Ok, found a solution: Don't run from a Desktop icon. I'm using a shiny new button pinned to the start menu.
UAC in Windows 7 has a protection scheme that prevents drag'n'drop between applications of differing privileges. Desktop apparently has a different level than explorer proper, so it won't do it. In theory, UAC being disabled should be the workaround, but it was already off. UAC has more options in fancier versions of Windows 7, but not Home Premium, which I'm running. So, should anyone else run into this, there ya go.
As an added bonus, my media keys now work in the Maya window.
For further value, this thread was first hit on google for searches on this. Go PC?