Is there anyway to keep glass from splintering when you drill it? I had it sandwiched pretty tight between two blocks of wood and I still got a fair bit of splintering.

I keep tape on it and like you , drill with wood backer clamped on and get along pretty well . Slow n easy...

Then I use a small  about 1/2" grinder ball on holes to smooth up. It is just an abrasive stone type.

X2 on  what  Kenny said. I will add you could put overlays on the limbs before you drill.

Use sharp bits tape and backer board dont rush it.