A friendly, bidding war among passengers to free up seats voluntarily, would have resolved this. This whole thing was a huge horrific mess, no matter how you cut it. Airline industry is becoming a thug arm of TSA..... Who the heck to they think they are physically assaulting a paying passenger who has taken his seat!?
I agree. Everybody has a price. Any amount given for volunteers would be worth it compared to the losses they are incurring now.
Include 5 free upgrades to 1st/Business with the money and you'd get some volunteers.
And it costs United virtually nothing.