Is this a brag post?
About the river... If he can do it with AK it's a call regardless of what else he's doing it with. After 6k hands with him you should have at least an idea if he can do it with AK, but the important thing here is frequency;
For instance if he'd only do it with the suited AK (or 25% of the time with AK) it's a fold. If he does it with all AK it's a call.
Also... This is highly opponent dependent so you might have a better idea about it than we do, but I'm not sure the question is about the river. Think it's really about the turn. Unless you have a read about him giving up his bluffs with overs in 6bet pots after 1 barrel, calling turn and folding blank river seems like it's burning a lot of money. The fact that it's a 6bet pot and that you're freaking 400bb deep makes this a huge decision, but you should not call that turn bet before you know what you'll do on the river if he shoves on a blank.
And if your line would be to fold to such a shove, then ask yourself how often he'll give up, to justify you making the call on the turn.