The diplo hit on digging up their stuff is only if a) it's inside their culture borders, and b) you do it twice (like spying)
The best way to avoid a problem altogether is to dig a site that's near to their borders, so it's likely to be a site where they won/lost a battle or found a ruin, and therefore be 'their' artefact, but not actually within their borders. It's best cuz you may not even have to get OB, and if you've tech'ed well and hit archaeology nice and early, then there will be lots of land still not subsumed into culture borders.
If you do it once, and then send the next dude into another realm, that's the 2nd best strategy, although it is POSSIBLE (I haven't tested this yet) that they might still class it as 'theirs' if it was THEIR battle/ruin, just in someone else's border.
Kinda like promise you won't spy on them anymore, so you move the spy, but then they think (glitch/bug) that the spy is still there, right?
Realistically, for Deity CV you only need 6 total artefacts. Chances are you will have enough matches of era that the theme in the museum will give you a bonus, and at the same time have enough variety that you can get the bonus from the Louvre, if you got it. And I rarely see the AI take exploration unless THEY are the tech runaway (in which case the chances of winning by CV are low anyway haha).
My 40 or so games on Deity have taught me 3 things about victory conditions:
1. The order of difficulty - in reverse order = Science, Diplo, Culture, Domination
2. How much fun I get from playing them = None, Little, Some, Lots (respectively)
3. How many of the best players in the world actively seek them out = Some, None, Little, Lots
And I champion the Swedes as a surprising dark horse for all-round wins. Very strong.