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Do you know of any adhesives that would work? I picture a some sort of yellowing glue that would look like crap. Something that dries transparent?

Seems like there would be something....hmmm.
The other option would be to drill holes in the glass and use nuts and bolts with those thicker runner washers on each side of the glass - drilling glass takes a bit more patience than I have yet to accquire, though, soo...

Holes would work, but then you have four bumps on the surface. Not the best for when your drunk friend puts his drink down.

Exaaactly!