By shoving here, you are trying to get one player to fold a few combinations by turning what is nearly the top of your range into a bluff. You are risking too much when calling gets you better results. I think you are being optimistic about folding out sets 100% by check-shoving this river against almost any two opponents (possibly for slightly different reasons). I know it's possible some people will fold slightly better hands, and I know strong players probably should fold a set here against a player who they view as completely straight forward, but it just won't happen often in an actual poker game where everyone has 6+ tables of 6-max running and sees they're getting check-shoved on and getting great odds on a call with the third nuts and so many other events having to line up for them to be against a better hand (would you ever check-raise KJ here, could you ever turn a hand into a bluff, I have great odds and a set, I call!).
I don't want to say your idea is poor in principal, but with such a strong hand your options are quite different than if you had a hand more similar to Q
J
here.
Option (1): Call $325 to win $1170 probably close to 80% of the time.
EV = 0.8($1170) + 0.2(-$325)
EV = $871
Option (2): Risk $1130 to win $1170 85% of the time.
EV = 0.85($1170) + 0.15(-$1130)
EV = $825
Option (2b): Risk $1130 to win $1170 90% of the time. This represents your view in OP.
EV = 0.9($1170) + 0.1(-$1130)
EV = $940
I am in agreement with most in the thread that people just aren't folding 99 here and nobody mentioned that really only one person could have 99, which would change our 85% chance to win the hand in "Option (2)" and 90% chance to win the hand in "Option 2b" to a number closer to 81% or 82%. If this is the case, calling is clearly the correct play. "Option 2b" represents your optimism for folding, which I believe to be incorrect. If somehow it were true, then you are correct that check-shoving here could be more valuable.
For turning your hand into a bluff here, you have to win the hand far more often than you will given that the second Villain will have KJ much more often than a set and that both Villains will almost never fold a set, as exemplified by the responses in the thread and by what I have seen in practice with timing, especially facing such great pot odds.
Feel free to make the EV equations a bit more complex with different assumptions about Villains in the hand. For our purposes and in this situation, we lack information to make a more complex equation that would be any more accurate or meaningful. The crux of the problem is how often they have KJ or if Villains will ever fold sets. There is also something to be said for showing people that you're willing to turn literally any portion of your range into a bluff at any time. That will make plays like this far less likely to work in the future than if you were called and had JT or another clear raise or fold hand facing this action.