That seems like a wonderful collection! Endless hours of listening pleasure!Last year I made these two birch ply CD racks. Each accommodates around 500 cds.
Size is 4 ft by 2 feet with 6" deep. Material used, one sheet of ( 4×8 ft) 12mm birch ply and 3mm ordinary marine ply sheet for back side. No need of veneer as birch itsef has a nice grain. Teakwood patti for front side.
I think I need few more