I just scanned through everything from D1 and I can't find anything else that references how long it took for the Horadrim to catch the Three.
There are other sources which say the Exile lasted many decades, so that does seem off compared to "countless centuries", though in a medieval society anything more than a few generations can get distorted pretty quickly, so it seems like a fair error, in-universe.
Re: Mephisto being buried under Eastern sands; while we know he was caught in Aranoch, then transferred to Kurast, we don't know when that happened. I would assume it didn't happen until after Diablo was caught, at the earliest. Anyway, wasn't the fact he was transferred first established in Diablo 2? And there's an in-game lore tome entry, The Tale Of The Horadrim, which repeats that almost word for word, but I can't find anything from D1 that says otherwise.
That brings me onto something else:
Hratli (after being given The Guardian quest:
He doesn't seem to agree with Sankekur. Hratli's no fan of Zakarum, but taken at face value it supports my theory that Sankekur's letter is false righteousness to cover his own corruption. That's also supported by Zakarum appearing (according to the D3 timeline) just as the Horadrim faded - it doesn't make sense for the Horadrim to specifically entrust the soulstone to some upstart new religion as Sankekur implies, but if Zakarum just took over the abandoned tower (as they did Tristram cathedral), then the events leading up to Diablo 1 were just history repeating itself. It also helps explain how Mephisto corrupted Zakarum so quickly and easily.Mephisto, along with Baal, was originally captured in the desert near Lut Gholein. But imprisoning two of the Brothers together was far too dangerous. The Horadrim built the Guardian Tower to hold Mephisto. When Zakarum came to power in this land, it took over the Temple City without paying any heed to what was locked within the Tower. And it became their doom.