An Odd Glitch (Perhaps in Wordpress) That Maybe Someone Can Explain

Over the last two or three days, one of my Wordpress sites has gone berserk vis a vis what time it is.

I schedule most  of the posts at Rational Review News Digest ahead of time so as to spread them out over the day without me having to be at the computer pressing "publish."

In Wordpress preferences, I have the time zone set to US Eastern Time. The server's default time zone is US Central, but Wordpress overrides that.

Thing is, now it's jumping around. I'll put in a post, go to schedule it, and my screen may tell me it's the time it is (say, 1pm Eastern), or it may tell me that it is 3pm, or 5pm.

Even if the time it says is correct, a few minutes later I may find that my post scheduled to publish an hour or three hours later has already published, as have all the intervening posts, and maybe some after that one ... and it will say it was published at the time I specified, and when I go back to the post entry form, it will now be telling me that it's four hours later than it is. And a few minutes after that, the time it reflects will be accurate again.

I've checked the server time in my hosting control panel, and it seems to remain the same, accurate to its own set time zone.

I haven't added any new plug-ins lately.

So instead of RRND's content rolling out in an orderly way, it's posting in big chunks all at once (and auto-posting to Facebook, Twitter and Google Plus in the same disorderly manner).

It's pissing me off.

Is anyone reading this having this same problem, or perhaps has had it before and figured out how to fix it?