I don't like betting rivers, the only thing we are trying to do is get value out of Qx hands, maybe some mid pps. If I have Qx (as the villain) heros large river bet is a weird line that I would typically fold to as it seems to be something that usually shows up as a nut or near nut hand. So hero is basically only getting action from a J.

If we bet small we are more likely to see some calls from Qx, but we are also going to be raised by Jx always, and the rest of villains range sometimes. I don't think hero wants to call that raise ever unless you have a really specific read. Qx may also just fold anyway. I mean why have you awaken now at the river? what hands call this flop and turn that don't beat Qx. Villains should expect to split (at best) or lose if calling that river bet.

Checking the river therefore seems like the only logical action for me, and my plan would be to c/c though I would probably tank/fold to larger bets or shoves most of the time. Reasoning being that your line here is pretty spewy, especially turn, if you don't get to showdown. If villain bets river small, you're going to be +ev if you win just ~20% of the time. c/r river is always spew.