We had the same issue with a Deep silverware drawer. We made a double decker,no wated space,and covered the Fac. plywood edge with Real cherry wood at the same time. Youroo!!
Agreed the drawer is deep enough to double up and that is an option we are keeping open. The bottom layer will not be as convenient so it needs to be just the right stuff. When we ID the right stuff we can put rails into the drawer to lift the silverware tray.