It might not be very convenient, but what about just slicing up some thin cardboard to place between each dish? You could also go to any self-storage place and buy a "dishpak". It's a package of bubblewrap sleeves that you place individual bowls and dishes in.
This might sound a little crazy, but once you pick a suitable "shim" to place between the dishes, perhaps you could find some sort of light duty, elastic strap to wrap around the bundle of dishes?
I think I understand the issue- it's not one of breakage, but perhaps an issue of noise from the dishes rattling in their storage?
Aside from newspaper or bubblewrap sleeves, I'm not sure what to suggest for bowls and glasses.
S/V Old Shoes
1973 Pearson 30 #255