I had to post here because it seems that W3TC doesn't just break the post scheduler function, it breaks MOST other scheduled functions.
Since it's update my WordFence Security plugin can no longer make scheduled scans, UpdraftPlus backup plugin has a confirmed problem with W3TC preventing scheduled backups, and at least 2 of my other plugins that have cronjobs or scheduling have had their functions seriously hobbled.
This is ridiculous. Tonight I just deactivated W3TC and installed Quick Cache (WP SuperCache is also known to have a few issues with WordFence and also Updraft). Speed tested my site before & after on GTmetrix, speed actually improved. Waiting to see if any of my scheduling functionalities with my assorted plugins returns....either way W3TC will NOT be returning to my site.
I understand some people are married to W3TC but I'm just not.
BIG thank you, though, to ptnplanet for all of the analysis and workarounds/fixes that he has provided in all his linked posts.