I disagree with bolded as I believe most live players are snap calling with any big draw on the flop FD/OESD.
I think the sincere tank flop call is more indicative of a gutshot, Tx, a hand like JJ, 7x. And then, like you and others have pointed out, the turn snap call most likely means that marginal flop call picked up a diamond draw.
River play: Now a lot of that range missed everything by the river, and 7x probably isn't even calling a 1/3 pot bet. So on the river, assuming we don't have to worry about a bluff-raise, it's between betting small to target hands like JJ/Tx or check/calling and snapping off bluffs. In my previous post I advocated bet/folding attacking JJ/Tx, but that could easily be bad advice if villain has a decent bluffing frequency in this spot. In fact, given that this villain is already down a lot of money, and thus probably more likely to bluff, I suspect check/calling the river is probably better.
So yeah, I'm now going against my previous post, lol. I should've read the OP better (I somehow missed that villain is down alot).
But either way, imo, it's close between bet 1/3 pot or check/call.