Somebody is going to get killed from this.

For sure.

If they’ve got a problem with non-emergency callers dialing 911, surely it would be best to try and reduce that problem through other means (such as fining persistent inappropriate use of 911)

I don’t want to talk to a fucking robot when I’m on the floor dying.

I think the non-emergency number should be heavily advertised. I have no idea what the local one for me is (if it even exists)
What happens if you put “police your_city” in your favorite search engine? I tried it with my current city and the village where I grew up, and both led me to the phone number in reasonable time.
That does work (actually ‘non emergency city state’). But as another comment mentions, the public knowing it exists is more important than the number itself.