When switching the beetle tray to a new tray I remove the pupae tower and then tip everything into a spare tray. I tip everything into one half of the tray and from there I use a baby spoon (because it's nicely rounded with no sharp corners) to pick up spoonful of beetles, or whatever, and drop them in the other half. Live beetles will move, dead ones won't. I can then pick them up and drop them back into the beetle tray.
It's hardly a quick process but seems to work OK.