Most of their problems, as usual, seem to be gate agent related, so they need to move away from them as much as possible. They need to automate the majority of the overbooking process by updating their site AND app with an oversold mode that will automatically offer an option for an alternate flight and compensation if the flight is oversold (and maybe put more kiosks around the gates for people who don't have the united app so that they can bid to get bumped from the flight).
I'm sure a lot of people would be willing to be bumped for compensation, but some newer flyers may be unsure of the process/connections/outcome, while others that are willing to but don't want to waste time sitting around the gate, waiting for the announcement, and having to line up only to be told that they found someone/don't need anyone.
They can then automate the whole process with a bot so that they can predict if a flight is oversold and automatically start offering people money and maybe a free upgrade on an alternate flight until someone accepts an offer (maybe even offer cash if no one is volunteering since they'd have to offer cash if it becomes an involuntary bump). The winning pax can then go up to the gate agent and have them finish up the process and issue the new boarding passes and vouchers/cash.
I always volunteer, but am usually in the lounge so forget about the whole situation, so I think something like this could help them find more passengers willing to give up their seats.
If they wanted to go to even further, they could make it into some sort of game/lottery so that people who might be willing to be voluntarily bumped can enter to win some sort of prize package if they "win" and get bumped to a different flight.
tl;dr - They need to update their app and site so you can 'bid' to get bumped, and *probably* never have to do an involuntary bump.