Could you not still, even with the way it is, somehow attach it more permanently? Starting with its original center point, then molding up the putty on the tops of the wings to harden against the glass?
I'm not sure how strong that mighty putty stuff is, though. The only way I could be 100% sure what to do, is if it was my table. I'm kinda hesitant to tell you to do anything that would permanently mar it.
EDIT: If it were mine, I'd be pondering getting out a drill and a glass-cutting bit.