Airlines could fix this by numbering the overhead bins and issuing a limited number of tags for each. FC & Highest elites would get theirs for free by printing it along with their boarding pass (or getting the hard copy from a GA or machine by showing their PDA with boarding pass screen) >>Likewise those seated in bulkhead ELR (by status or by paying would also get their tags assigned. Next, mid level elites could purchase space available for a discount when doing OLCI and pay for the overhead luggage tag along with their checked luggage fees. If there is any overhead space left one hour before the flight it can be sold to non-elites.
All bags without overhead luggage tag for that segment would have to fit under the seat or be gate checked. When passing the gate, all items carried by each Y PAX must fit in an under seat seizer or have an overhead luggage tag. CO-UA should be able to generate enough extra $ when the average PAX decides to check many items he now drags on the planes which slow the boarding process down> This has become a bigger problem since they started charging for check luggage>> Now even thing up and charge some PAX for carry one. Also if you do decide not to check luggage that will not fit under the seat at the counter hoping to sneak it on (contributing to longer loading times) the last minute gate check fee should be higher that a discounted fee at the non-airside counter.

In fact part of the elite package each year could be a overhead luggage tag holder/elite tag that elites could attach to their carry one luggage and insert their overhead bin tag.

This would be a win-win as elites and those who choose to pay would have precious reserved luggage space reserved no matter then you board, the airline would make extra $ and planes would board faster as most PAX would not attempt to drag oversized luggage