I think your preflop 3bet is way too big. That's the only reason you're going to end up having to call here. You can easily make it 850 with much more maneuverability.

Once we make it >1k, I think it's hard to fold. I think 3betting pre is fine, but the reason you have to call is because you made it a sizing where your opponent would struggle to 4bet/call or 4bet/fold. I might be inclined to 3bet/fold if he made a small 4bet because that would be much more weighted towards trappy hands, but when he backshoves like this I just can't give him credit for KK+, which is going to almost certainly make this a call.

Once we get shoved on, the pot is 9907. We have to call 6965. 9907+6965 = 16872

6965/16872 = 0.412. We need 41% equity. If we give him JJ+ AK+, we have nearly 43% equity. If we discount KK+, we have around 48% even if we add some lower pairs, and obviously if we add AQ our equity is going to shoot up. It's a crappy, high-variance spot to get in this early in the Million, but we can't fold, and if we 3bet to a smaller sizing preflop we would have a lot more options.

In a lot of ways you're right, but I just don't think this is as thin an edge as you're assuming it is. The Sunday Million happens every week, it's not the One Drop where we have to be incredibly careful about risking our whole stack because the ICM value of everything is massive. Yes, it's completely true that winning this pot doesn't affect our equity in the tournament as much as losing it does, but considering that there's a probable 7% gap between the equity we need and the equity we have, I think that's far, far too big of an edge to pass up.

We obviously can't rely solely on math for making decisions, but we also can't turn down spots that we can prove are extremely profitable based purely on the possibility of gaining future equity. If we continually turn down these extremely profitable spots, we're neutralizing whatever future equity we have, because our equity in the tournament comes from our ability to make good decisions. Turning down a 7% equity/pot-odds advantage is not a good decision in any spot. If we could guarantee he did have KK+ in his range here and never ever had AQ, 43% equity might be thin enough for me to find a fold, but not a potential 48% or higher with KK+ out of his range.

Incidentally, I still maintain that the key issue here is the 3bet sizing, because the fact that we're facing a decision here is a direct result of 3betting way too big.