Honestly, I'm not convinced that either of those series qualifies as essentially ordered and I'm not sure you can find an entirely unambiguous example that's purely physical. I'd regard those as illustrations (intended only to get the point across) rather than proper examples.

I'd recommend instead something like an audience listening to a song being played by a musician. When the musician stops playing, the song stops being played and the audience stops listening (and starts merely remembering or anticipating). Part of what makes this work as an example (rather than just an "illustration") is that a "song" is (in my view) a higher-order reality that can't be cashed out in purely physical terms. At any rate it's somehow related to the intentions of the musician and the audience: the musician is playing the song for precisely as long as s/he intends to play it, and no longer; the audience would cease hearing the song as a song if e.g. they stopped listening, or were struck by a disorder that interfered with their ability to comprehend music the way some disorders make us unable to see faces.

It also has the the (to my mind) inestimable advantage of getting to the heart of what I think was St. Thomas's real understanding of such series: that they involve, at the first step, making something "be," and at later steps, passing that "being" along to the next member of the series. Ultimately, that's what St. Thomas cares about anyway (as Ed Feser argues quite effectively in a piece included in the best bang you're ever likely to get for your twenty bucks).