I have not tried this yet, but I have the same problem and this is the approach I plan to try. There is a special Tenax peg that was originally used on the (rare) cars with aluminum windshield surrounds. The peg was unobtanium for many years, but TRF has recently had some of them reproduced. This peg is designed to go all the way through the frame, with a countersunk head on the back of the frame. The screwdriver slot in the head will be visible, but otherwise they look nearly identical to the originals.
P/N 553837
http://trf.zeni.net/miniTR2TR3/58.phpThe trick will be drilling and countersinking the frame without hitting and breaking the glass. A depth stop on the drill bit(s) seems like a requirement; and I'm thinking that a simple jig might be a good idea as well. To help keep the bit from grabbing in the soft brass, I'll also dull the cutting edges just a bit (or just use an old bit that is already somewhat dull).