Scheduled posts publishing early/erratically

Who is the webhost?

Media Temple. Has been for a year, but the issue just began. Support techs didn’t have any answers as to why it would start doing that.

It’s really a server thing. You can try running WP cron manually: https://www.ads-software.com/plugins/wp-cron-control/

Does the interval matter, as long as it’s being run through the plugin? Also, MT’s kb article for cron jobs says “The cron will use the PST time zone.” —?does that matter, since the intended post times are in EST?

Try compensating for PST with your scheduled post times. This is really a host thing. You need to get more details from MT on what they do.