None of the basic rules apps working - they use to, but not anymore

I think you are on the right track with your assessment of the logs. From @bobbyD 's post on the topic you linked talking about updates to logging of scheduler errors and the notes in the Release 2.3.7 topic, I expect what you are looking at is the update they made to make this troubleshooting easier, i.e. the Past Logs where you saw an error for App 302.

I suspect simply disabling the app, however you did that, was not enough to result in the scheduled job to not be impacting the scheduler. I don't have any Z-Wave devices, so am not familiar with the Z-Wave Poller built-in app, but from what I can see you must setup a scheduled poll of devices. Could you temporarily uninstall this App and see if that corrects the scheduler issue? Then re-install the App?