Meh. Even if the transition to a 128 bit time value takes a billion years to roll out, it's no big deal. There's no reason to think it would be drastically more challenging for whatever intelligence to deal with it then than it is now.
Git blaming code from billions of years ago would be hilarious. Imagine understanding the few hundred keywords in a long-lived language but not being able to understand the git commit messages.
In reality, 1,000 years in the epoch will be just arbitrary. By then they might as well pick a new epoch that isn't 128 bits. What would they need to preserve that they wouldn't be able to emulate or virtualize?
One interesting idea in Vernor Vinge's A Deepness in the Sky was the job of "code archaeologist". A far future society, they were saddled with ongoing maintenance of centuries-old code, and needed to be able to figure out what those historical programmers were trying to do.
Held that title (unofficially) in a company. Figuring out "what did we mean by this, twenty years ago" was already a nontrivial task, even with a theoretically similar tech stack.