[2NL] TT OOP facing river decision

One thing with your range: you can't really take away all FD from his range ott, because he has FD+overcards or combo draws also. Do you really think he would fold stuff like Qd9d, 9dTd or a combo draw like 6d7d ott?

Also if he is 38/20 with 50% steal, I'd think he would open most of his PP preflop on the button, certainly stuff like 88 and 99.

Personally I am struggling with pokerstove to get you more than 50% equity vs his calling range, maybe Spoon and Imsavy can enlighten us with their ranges:

Code:

Board: 3d 4d 4h 2s Kc
Dead:  

    equity     win     tie           pots won     pots tied    
Hand 0:     51.429%      51.43%     00.00%                 18             0.00   { ThTs }
Hand 1:     48.571%      48.57%     00.00%                 17             0.00   { 77-22, A5s-A4s, 65s }

and that's assuming he calls a shove with 55, 66 and 77, and assuming he would fold A5o-A4o preflop, so it seems a bit optimistic. I also didn't give him 64s, 54s and 43s which are not impossible. You could argue that trips would raise at some point, but I am not so sure, why would he if you keep shoveling money to him (facing a probable overpair, there is not much for him to fear from draws).

So in the end, I am not so sure about shoving. Is c/c horrible here, as it gives him the opportunity to bluff his busted draws?