Well, for the interim I got some 1/8 foam core board. I think it does make the radio sound better. While the radio was playing I touched the back and could feel it vibrating like a speaker cone.
I still have to cut out a couple of vents for the receiver compartment. That's only about 12X12 inches and the rest is just open cabinet space, so thankfully i won't have to do too many cuts to get adequate airflow.