It’s also possible to “freeze” your employment history report just like you can freeze your credit report. Which prevents even companies with the wherewithal to do an employment history check from getting that information.

Interesting, how do to that "freeze"? I thought it's all data brokers I don't have any leverage on.

You have to do it via a mailed-in form, but I did, and got a confirmation letter back. I haven't assessed the efficacy of it, but supposedly mine is.