He's last to act and checks the flop, giving everyone a free card. On the turn he raises to a bet and a call. What hand does that? I think that's the most important question, because the closer you get to figuring out what he could have, the more chances you have to get the most value in this hand.
Would a weak K (KQ, KJ, KT) raise this? It doesn't make much sense checking the flop when last to act, then raising the turn with such a hand, but I guess it depends on player. I really doubt he has that but if that's the case, when you call his raise and then check the river, he'll check behind, so your strategy won't work.
If his weak K is Kx both spades, if he misses his flush, again I think he'll check behind on the river. Such a hand could explain his line so far. So would, maybe, As7s.
Could he have AK? He didn't 3bet PF. This is $100nl, I don't know if the average player in this level always 3bets AK, nor do I know if you have any reads on villain in this sense. Also, if you think he'd slowplay it on the flop. This is important IMO because AK will likely bet the river for value when you check to him, but I can help to think that it just seems too odd to be AK.
The only possible 2 pair on that board is K7. Could it be a flat call from MP3 with K7? With 4 players left to act? This also seems odd.
I think any medium pair that flat calls this PF would bet the flop when checked to, and it certainly wouldn't raise the turn after a bet and a call, so we should be able to safely exclude that type of hand. Any pair JJ+ would 3bet PF, so unless he's tricky (like flat calling with KK) those hands are also excluded.
Last possibility is a bluff. Against that, your line of calling then checking the river works best because he might fire again on the river.
A set bigger or smaller than yours plays itself pretty much so its pointless to talk about. We're discussing about getting value from hands that you're crushing up to this point.
The big issue is that, if you 4bet it now, say to $45, you're giving away that you have a strong hand and in most scenarios considered above he will likely fold. The only one that calls and maybe shoves is the Kx both spades, which, IMO, is also the most probable hand. So I'd raise it, even if it gives away the strength of my hand. In a certain way, the flat call does also, although, admittedly, not to the same extent. But the main reasoning to raise now is because it might be the last chance to get more from him.
I understand your argument that MP1 has been c-betting a lot and MP3 has been playing position, but because this pot is 3-way I think I'd lead out this flop. Not every player c-bets in 3-way pots and I think leading out is best because on such a board I doubt they would let you take the pot w/o at least 1 of them calling a flop bet, and you could even get raised if one has a strong K, which sets the stage for you to possibly call and the check/raise the river. It sucks to flop a big hand OOP rather than last to act but in multiway I believe leading out is always best, unless they are both very aggressive and you're absolutely certain they will fire away no matter what. It's true they could both fold to a $6 bet but I still think leading out is the better play. Just my 2c on that.