Sounds like quite a pickle.
Ice and PH are the only 2 safe ways I know, besides carefully lifting if you can do w/ out tearing such as on glass.
No way to rig like a coathanger or something, maybe freeze a piece of ice onto a bendable something that will reach(and of course not stick it or tear it w/ this bendable whatever)
Personally, if it were me, I'd probably just buy another BTA and stick that one where you want it.
But it is true what everyone says, they do have a mind of their own, and go where they want.
Chances are those will move...someday.