Would it help to have the countdown load somewhere else on the page - a banner or <h1> tag maybe? Google is only listing what they find there between the <title> tags.

What you really want is to show the underlying “base” content to G, and show something else to humans, keyed to the exact time of their visit. If I knew how to do that without running into charges of Cloaking, I’d be a lot richer than I am.

Your situation is not unique, incidentally. We’ve all come across search snippets where the displayed text is obviously not what a human would see on arrival--and, more to the point, isn’t what the site would want anyone to see, whether visiting or searching.

Strictly speaking using the title tag for the purpose described is not what it is intended for. A title tag is not meant as means of user notification. I know it is used for this by some websites, and web-apps (Slack being one popular example), but it really is not its intended purpose.

Google will do whatever it does and there is generally little you can do to stop it. The fact that Google takes whatever is in the title tag remains consistent with intended purpose, that is as a title to identify the tab/website.

You could use other means of notifying user, such as using push notification.
[developer.mozilla.org...]
But of course, this requires the user's opt in, and is not supported by Safari. (Apple's continued attempt to keep it's grip on the app-store)

use a Disallow directive in robots.txt to exclude googlebot from crawling the javascript file that contains the title tag editing code.