I think its a cool spot, thought about it for sometime and here is my opinion:

Lets say BB has a pretty tight 3-bettor BBvsBTN which most players are in PLO50z. His range should crush this board, when he checks flop I think it quickly polarizes his hand to a checkraise monster or a hand a hand that has showdown value that doesnt want to get raised. If he has naked Aces or Aces with an 8 he is proabably check calling this flop. If he has somethink like AKJ7ds hes proabably check calling the flop. When the turn is a jack and he bets around 80%, to me, it looks like either KJxx, AA with some backup like a T for a nut gutter that wants to protection bet, or just a hand like AKKxss that wanted to slowplay for some reason. Other than this you have the random stabs like a bare flush draw, gutter with a J or just AKxxds or something wanting to protect. I think its a pretty standard call here in your spot with the two pair + open ender.

On the river though, I feel like we want to have a king to bluff (eventhough we might be overbluffing betting a king here?) just because he is always calling us with AK+ on this river if he doesnt have spades. Having the QT here I think is bad for us as well because we want him to have all of the pickedup-wrapcombos on the river.

Can someone come up with some hands that we check back flop with on this board, calls turn with and can bluff river blocking some KK, AK and AA combos with? I think people here are overcalling in this spot too so having a 3 makes it an easy value bet imo.

I think you're getting looked up on this river very often. Likely by KQ+ which I think is the majority of villain's range when he checks the river as he'll often bluff with many of his hands w/o SD value. As such I don't think you should be bluffing often here. If you are worried about balance in this spot, which you probably shouldn't be, I think you will make it to the river with some hands with an A blocker and some missed draws that make better bluffs. QJ has some SD value and is only trying to bluff AJ and KT, with AJ only representing a small portion of villain's turn betting range and KT representing a very small part of his preflop 3B range. If you're gonna bluff, bluff with the hands w/o SD value that benefit from villain folding most J's or 8's

I think villains range is full of Kx, AAx and a lot a flushdraws, that you beat anyways. Additionally, it would be a good idea by villain to mix in some x/raises.