Outside CA, large tech companies tend to interpret a "competing company" to mean "another tech company", or at least they try to advance that interpretation (courts don't always accept it). For example, IBM's position is that a non-compete prohibits you from working in any field of endeavor that IBM works in, not only the specific one you previously worked in at IBM--- and IBM works in quite a lot of technology areas.

Related: A decade or so ago, I worked for a small company that was acquired by Lucent, and part of their legal paperwork involved assigning any IP we created that was relevant to Lucent’s current or future businesses. A co-worker of mine observed that according to this document, if Lucent got into the Web content business, it would own his personal Web site.

That's a good reason to write an addendum that defines "competing company" and "related business" in very narrow ways.

Employers have reacted more favorably to addendums rather than crossing out clauses, even if the addendum practically neuters the entire document.

Hmm, that's an obvious-in-retrospect approach I hadn't thought of. Just try to submit an addendum that defines the relevant field as something that isn't absurd-sounding, but is quite specific to what you're being hired for, and therefore clearly excludes wide swathes of things that aren't that.