I bought a barrel last fall, haven't started on mine yet, waiting for warming and longer days.
I was thinking about getting a diamond tipped drill bit and drill four holes in the glass, then secure the glass to the monitor back board (?) with bolts and maybe spacers shaped like barrels, between the glass and the board.
The diamond tipped bits aren't as high as one may think, although I am not looking forward to drilling the holes in the glass. (Google it, there are tutorials on how to do it.)
I may check with my local glass shop to see if they can do it.
I also like your idea, yotsuya, of keeping the glass inside the rim of the barrel, although I think the way griff did it would look better?