“Why are there so many dead bees on my screened inner covers?”
I can’t be certain without doing an experiment, but I believe most of the dead bees on your screened inner covers are robbers who died trying to get into the hive. First of all, robbers don’t know where the hive entrance is. Instead, they follow the scent. If the scent of honey is drafting out of the top of your hive—especially during a late summer nectar dearth—robbing bees are going to pick up that scent and try to get in at that point.
This is similar to the bees that follow the odor of honey that comes from my kitchen every autumn when I make barbecue sauce. The fan is ducted from my stove hood, through the attic and comes out at the other end of the house. When I cook anything with honey—and the barbecue sauce contains a lot—the bees form a cloud where the air exits the duct.
Sort through the dead bees and see what you find. Mine are always mixed with yellowjackets—another indication that robbers are looking for a way in. Yellowjackets and other wasps do the same thing—they follow the scent to find the source. And once bees start dying up there on the screen, the yellowjackets are even more interested. I’ve also found other things on the screens, including wax moths, spiders, and various beetles.
However, it is very possible that some of the dead bees were residents of your hive that couldn’t find their own entrance. This would be especially true of first-time foragers or bees out for an orientation flight. For this reason, I think it is best that the shims for your screened covers are in the front and back, so that the smell wafts out the sides. If the shims are on the sides, the smell comes out the front and back. Hive smell coming from the front is probably more confusing to the residents and more advantageous to the robbers since it is closer to the hive entrance.
Some of my screened inner covers have shims on the sides, and some have shims on the back and front. I’ve never noticed a correlation between dead bees and the location of the shims, but now that I’ve thought about it, I will definitely look for that in the future. In the meantime, don’t worry about the dead ones. The excellent ventilation provided by screened covers is more important than a few bee losses . . . and most probably those bees came from somewhere else anyway.