I seriously can't understand what kind of mental gymnastics this airline management is doing in order to justify in their heads that this is just fine.

Even if the law is on their side, they still overbooked the plane by themselves, they still let everyone check in, they still let everyone in onboard and they still forcibly removed some random paying passenger just because someone on their staff wanted/needed (anyone can clarify this part?) to board.

Here is an idea for United (your HR department can contact me, I'm available to hire for 50% of your CEO and I easily come up with much better ideas):

1 - you just have to simply get the attention of the passengers on the plane (if you can be a bit smart and do it OUTSIDE the plane it's even better).

2- keep increasing the compensation you give one (or the needed) of them in order for them to catch a later flight.

Sooner or later someone would just accept the compensation. Also, that compensation wouldn't be anything special anyway since you have a plane full of people competing for it. The passenger would be happy, United would get what it wanted and you wouldn't have this media shitstorm in your hands.

Yes... it's really that simple United (again, tell your HR department I'm available for hire).