I've generally considered Pete Carroll number two on the list by a somewhat wide margin, but there's just as big a gap between him and Belichick. For as much shit as he took for the superbowl interception, that he was able make that decision in an absolute pressure-cooker situation with the clock beating him down was pretty remarkable, and not something I think most coaches would have gotten. IMO, where they really lost the game was, ironically, a breakdown of discipline. They actually had a top flight D and NE stuck in a terrible position, and they let Brady draw them offside. That was worse than the play call, and it's something that NE would never have let happen. Still, the dude's an excellent thinker, and he always finds a way to make do with what he's got, which seems to be less and less each year.
Payton probably has to be number 3, and then there's another big gap.
I don't have a better pick for number 3, but for some reason I'm surprised you put Payton at 3. Though I suppose that's probably the best indicator of the size of the gap, because Payton is closer to Reid than Belichick when talking about the tings we're talking about (discipline, etc.). I think it's partly on Payton that his team basically collapsed after the missed pass interference call last year. That's partly the coach's job to help keep the focus.
As for the Patriots/Chiefs, I understand the "Dee Ford" line of thinking, and it's tactically correct, but strategically flawed. First, that's not an "official's judgment" call. It's a dead ball foul, in the sense that he was lined up that way prior to the snap, and can move if need be to reset his position. It's on the Chief's. Second, IF you are going to play "what if" (which I'm not a huge fan of; we can "what if" David Tyree didn't have a huge melon head too), you have to go whole hog: why were they in that position to begin with? The greatest offense in the history of the NFL, MLB, NASL and the NBA combined didn't score one point in the entire first quarter. If I was more "superstitious", I might even say that Belichick got into Dee Ford's head; the offense wasn't going to win this game, the DEFENSE was, and they knew it. And, guess what, I'm superstitious enough to say that.
Plus, in the next game, the Patriots did the exact same thing; they faced a high flying offense, and made them play a different game (which they tried, and couldn't do). I think any other coach, and Dee Ford could have lined up in the parking lot and it wouldn't have changed the outcome one bit, but Belichick got his team in a position to win. You can contrast that with Reid all day long and it won't be pretty. (I've already gave you two examples including the Reid-coached best offense in the universe going scoreless for 30 minutes in their biggest game over the last 25 years at least).