Bees instinctively go to the top. They are bunched there because they are stuck and can not figure out how to leave. they will cluster together, feed each other, until they die.
I would remove the screen if you can. Let the bees fly off and your problem will quickly go away. Right now, you are just trapping bees, then wondering why they are there. Who cares! If they all die, are you not going to open the screen and clean the dead bees out? So do it while they are still alive and do them a favor.
It's a simple problem, and has a simple solution. Which takes about 2 minutes to complete, versus the two days of discussion that this has evolved into.