I'm torn between ck-f and showing him the 8c and shoving. More on the fold side.

Little deeper I think you can do well bet bet betting.

I don't hate it, but I don't think it works enough without a stronger read on V. There are some seemingly competent players who will never fold AcXc in this spot, and others who will fold everything except a boat, and we have no idea which group this V falls into. I also don't have overbetting the river instead of c/r shoving.

Its a unique spot... That is why shoving > check shove.
having J8 in your barreling range is extremely exploitable. There are enough spots that you get away with it on a 2/5 but none of them are standard.
Hero should never be barreling this wide 3way when main target is still a BB Whale. its too volatile unpredictable and simply an unnecessary asset to crush 2/5. We don't know yet how deep BB is but if he is 240BB deep this is simply a terrible noob move.

river spot doesn't really matter in that regard.

Grunch:

Check/raise bluffing here without reads seems like suicide and I probably don't attempt this without evidence a player has a fold button.

That said, villain is repping a super narrow value range like ATcc and/or is turning QTcc/off suit JT into a bluff. I assume vs normal 2/5 competition 9x usually gets a raise in at some point. The speed at which he calls flop and turn tends to make me put him on a FD or Kx. Most of the hands with SDV will check behind river or bluff busted draws. Since we block a lot of the conceivable club draws, we are left with monsters (which get a raise in at some point IMO) and weak SDV/busted draws that could never stand up against our line.

The question is: what are WE repping and is the villain competent enough to realize that we have a super narrow value range here as well? Would we ever take a b/b/x-shove line WITH K9/A9/ KK or AA here?

I totally agree with your last paragraph and that that's the most important question by far.

I slightly disagree w/ your first paragraph. I'd assume an unknown has a fold button unless I get evidence that he calls down postflop too often. I also disagree that he's repping a super narrow value of only A10cc, as he could easily take this line with 99, A9, or 109.

i don't like trying to check-raise bluff people off of trips

when you sit down at the table, what is your gameplan?
are you executing it?

Preflop is pretty standard to open J8cc in MP with bad players in the blinds. I might even open bigger to take it HU vs whale. Flop is a mandatory cbet although 3-way. Turn is the best barreling card to get him off Kx/flush draws. I'd bet again 100% of the time.

Well played until the river, OP.

I would just shove the river myself to continue telling my story. You've come this far, checking now is a big NO-NO imo. Just rip it in, and order shots for the table when he folds 9x face up.

I check/shove sometimes here against players who are capable of folding 9x. I know a couple of nits in my game who will also fold T9 (rivered boat) in that spot after tanking and tanking for ages. Just depends who you're up against.

Moral of the story: Once you start betting aggressively and miss your draws, you have to be pushing it in often to put them to the test. You can't wait for Aces and Kings to make that play.