I know that this is ridiculous option, and maybe impractical, but could they not make the overhead lockers lockable. They board the flight say row 15-20, all of the overhead lockers before there are locked, so people have to go to the back, then 10 -15 come on and the cabin crew unlock those over heads and so on. The least they should do is make sure that only CE passengers bags go in the CE overheads.
FP