"Your game designer works for a year and invents 7 games. At the end of the year, she sues you, claiming that she owns 4 of them, because those particular games were invented between 5pm and 9am, when she wasn’t on duty."
She wasn't paid for ideas, she was paid for intellectual property: code.
"hey listen, I know that inventing happens all the time, and it’s impossible to prove whether you invented something while you were sitting in the chair I supplied in the cubicle I supplied or not."
You don't need to prove whether something was invented while sitting on the chair. There's a pretty simple explicit transferral of intellectual property - you pushed it to the company github.
"that ONE GUY from 1998 who didn’t sign the agreement is going to be a real jerk about signing it now, because he knows that he’s personally holding up a $350,000,000 acquisition and he can demand a lot of money to sign."
Which happened when, exactly?