3bet pot OOP - What's our river bluffing range?

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3bet pot OOP - What's our river bluffing range?

SB: $125.01 (Hero)
BB: $261.81
CO: $192.07
BN: $51.08
Villain was playing with pretty taggy stats so far. Haven't played with him much before, so no real reads.
Preflop ($0.75) (4 Players)
Hero was dealt J Q Q T
CO folds, BN raises to $1.08, Hero raises to $4.14, BB calls $3.64, BN calls $3.06
BTN is raising ~70% of hands, so easy 3bet for value here.
Flop ($12.67) A 3 2 (3 Players)
Hero bets $6.50, BB calls $6.50, BN folds
My std is to bet this board with a small sizing with most of my range.
Turn ($25.67) A 3 2 K (2 Players)
Hero bets $19.50, BB calls $19.50
Was gonna give up when called, but now we picked up a straight draw, and this card is super strong for our range. We surely have a ton more KK combos than him after preflop and flop action, so our range is even stronger now at the top than it was on the flop.
River ($64.67) A 3 2 K 3 (2 Players)
Not the best river in the deck, but we still have a good deal on nut combos in our range. Should we be bluffing with our hand? What hands are good bluffing candidates here?

I think Kx hands are very valuable, since AK is probably his best bluffcatcher. I think weak Ax hands aren't really valuable as blocker hands, because his range after calling this flop 3way is pretty much exclusively Ax, and we already know he can't have aces.

Besides Kx, I think not having hearts in our hands is very good when bluffing here, since more hearts in villain's range means he can call with worse made hands on the turn (any AJhh, for example), and those are now very poor bluffcatchers on the river, not only because they are weak, but because they block our semi-draws.

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