Relevant song: https://youtube.com/watch?v=Z0JhC3LO0-8
I mean, these problems happen if you use offsets too, and my point is that they don't matter.
The most hardcore solution to those would be pre-computing pages but I doubt it makes sense to bring even more state to the search results.
Really? The underlying storage engine of most databases stores all data necessary for an "as of" query. Simply ignore all data pages newer than the timestamp cutoff, and prevent the garbage collection of any page that could be part of such a query.
In fact thats the way [eg. postgres] can do a long-running query on a table that someone else is modifying. You in effect are looking at a snapshot of the table at the moment you started the query, even if it takes an hour to produce all the results.