I was not sure how aggressive hero is and what villain thinks about hero, so I gave him JJ, TT and AQ as a call 50% of the time, as some of the time he would 3b/call those.
SO, Villains def range IMO looks like that (494 combos)
we cbet 372 into 870 (FE required 372/870=42%=207combos)
our hand eq is 43% - reasonably high, but our hand is best on 31% of the time
he calls and stays OTT with that (229 combos, folded 265combos so cbet of this size was indeed +ev) and our eq drops to 28%
we barrel 900 into 1614 (FE 900/1614=55%=127combos)
his range OTR (assuming he folds FD and GSs OTT and Qx 6x and stays with Ax, 2pair+ and pair and fd / pair + oesd, gs hands)
130combos (with this sizing OTT we needed him to fold out 127 combos, but he fold 99 only, so barrel OTT is
not profitable v his range, obv assuming we don't get there with our equity)
OTR, our hand is best 3% only. Looking at the board runout and the fact that he is not folding any Ax, betting river seems spewy. He calls 2675 to win 8764 needing 30% eq. I don't think he ever folds there.
So, according to math, betting OTT is a mistake, unless, he calls with gutshots and fd and you then you can check back river and scoop vs his missed draws.
conclusion: barreling vs fish that calls with gs and fd is fine. barreling vs reg that is kinda scared and folds Ax by the river is fine. barreling vs thinking player that knows that draws missed, you are capable of barreling and understands that he needs to protect his calling range and therefore will not fold Ax is not a winning play.
peace