Pre-flop sizing looks very good. Perhaps make it a little larger like 700-750, but since the fish is so short and you are on the button, I understand and agree with your sizing.
On the flop my gut tells me to call. No way raising is good being this incredibly deep. Folding seems too weak. But let's analyze this spot.
You are getting 1.7 : 1. GTO wise you should fold 59%, or call 41% of your range. Is villain too wide or too tight betting here? It is hard to say. He has a slight range advantage, so if villain is indeed a good player he might pick up on this and start leading. He is sizing up two ~80% bets to get all the chips in, of course he might not do this. But he is probably going to be very aggressive in this spot, maybe too aggressive. Because of this I'd advice to continue with perhaps a bit less than 41%, say 30-40%. Folding more would be way too exploitable. Let's see where your kings are at.
I'm rougly guessing here. But it is just to give you an idea. I think your range looks like this: 66+, A5s, AJo+, KTs+, KQo, QTs+, JTs, T9s, 98s, 87s. This is a total 174 combinations. You should continue with around 60 combinations. Hands that are better than kings: T9s, JJ, 88, 77, AA, arguably AJ. These are 31 combinations. You need at least around 29 more combinations, and you'd be already on the tight side. Include KK, QQ, KJs, JTs, maybe 98s, QTs with a backdoor flush draw. I'd fold TT and 99 since they block too many bluffs.
Calling with this entire range and not raising anything seems mandatory. You are in position, very deepstacked and your opponent is representing a very polarized range. Raising will not accomplish anything for you, except lose your stack.
Note: don't assume too quickly that the donk lead is weak or strong. He is a good player, so I assumed him to be balanced. Either way he is polarizing himself, so I wouldn't raise. If you think he is stronger or weaker call less and more combinations respectively.
So he shoves for almost pot. You need around 33% equity. GTO wise you should fold around 50% of your range.
I think you are overplaying kings here. I don't think you can raise for value. But if you raise kings, you can raise aces, sets, a straight. Kings are not in the top 50% of your range. You don't have to call and I think you shouldn't. I think you are always going to be up against a set or a straight. Villain would have folded his bluffs to your raise, he only has strong hands. He wouldn't do this with queens. You are nearly always beat. You can avoid the spot by not raising in the first place, but definitely fold to a jam.
I am guessing you paid it off and he showed you a set or a straight. Curious to hear what happened though.