Time zone change messing up newly set scheduled posts

I’m working on a site and we’re posting once a week at midnight. Originally the timezone was set at the default UTC+0 that WP installs with and since we’re displaying post times on articles and comments, it’s not correct for our timezone. So simple enough right? Just change to our timezone.
I checked out https://www.timeanddate.com/worldclock/ and set the timezone in WP general settings to UTC -5 (New York).

Well a post was scheduled today for midnight, after this change had been made a few days beforehand. The author created the post just a few hours prior to midnight, so well after the timezone change was made. And the post wouldn’t post.
He had to set the publish date to the day before today to make it post.

So, I changed the timezone again, selecting “New York” specifically from the dropdown menu. The post still wouldn’t go through.

I changed it back again to UTC +0 and he was able to post again right then and there.

Any ideas on what might be going on or happened? Thanks in advance!