Bedtime? Who needs it!
I think there can be lots of variations between the universes. For example, Cloud visiting Jessie's home in Remake. Whispers didn't stop that because it's not paramount to the future of the planet. But big things, like Cloud meeting Aerith, that's gotta be maintained. Their meeting is essential.
The Whispers might be "stretched thin", which might be why they allow variations.
Terrier Stamp is one of those variations. It's inconsequential! However, I think the storytellers included it to hint that Zack's scenes are happening in another universe altogether.
I agree with the page you linked to wholeheartedly, that the two perspectives could not happen in the same time and place. One is happening in the "Beagle universe" in December, the other in the "Terrier universe" in September.
I don't think that idea is radical. Let's use Into the Spider-Verse as an example. In that film, the universe of Spider-Man Noir, which takes place in New York during the Great Depression, is happening concurrently with the modern-day universe of New York that Miles Morales lives in. One universe is in the 1930's and the other in the 2010's, happening side-by-side. You wouldn't call Into the Spider-Verse a time travel story because the universes are independent. Additionally, Spider-Man Noir will not lead to Into the Spider-Verse. They're different continuities.
Given how Zack's scenes are always presented as happening at the same time as the party's, I think the multiverse in FFVII will function similarly to Into the Spider-Verse.
I think my usage of "time travel" was poor. I don't think anyone believes that Zack time traveled forward or something. When I say time travel, I'm referring to the interpretation that the party's past was influenced by their actions (i.e., Zack survived in the party's past because of the defeat of the Whispers). I don't personally think that's the case because it creates additional questions, like why show a new version of Stamp, but I'm also repeating myself at this point, so I'll leave it at that.
What I'm saying is that before the Whisper's defeat, all universes needed to follow the big events. So there were no universes where Cloud didn't meet Aerith and so on. But after Remake? It's all fair game. I believe this is exactly what Sephiroth wants. He wants there to be universes where events are allowed to be so different that his Meteor scheme succeeds.
Why? Because he wants the opportunity to win? True to an extent, but I think there's more. Look at the Edge of Creation scene. Sephiroth has learned that the planet with join "it" someday, leading to the end of himself and Cloud. Whatever "it" is, it sounds a whole lot bigger than the stakes as we know them from the original game. This is why I feel a multiverse is appropriate.
Alright, let's get real. It's been two years since the release of Remake and we're all solidified in our interpretations. I probably won't convince you or anyone else. However, I do hope I've laid it out in such a way that everyone can see how I came to my conclusion.
To put simply: the existence of two Stamps and the placement of Zack's scenes could imply to some people (only me?) that there's a multiverse. It's wild, it's new, but I think it's absolutely plausible.