Teams should always have the option to take the ball out from the sidelines instead of shooting free throws.
Thats one reasonable fix. You could tweak it and say in the last 5 minutes of a game the team has the option to inbound the ball or shoot free throws. This may also cut down on teams that are winning fouling a 3 point shooter before he shoots, because the team could just run a sideline set play to try to get a good look at a three.
You could also tweak the above so it is just "off the ball" fouls in the last 5 minutes (or 4th quarter) get the 2 free throws or inbound option.
A bit more extreme would be "in the last 5 minutes, off the ball fouls are 2 shots AND the ball."
Another fix would that would more address the specific "problem," but that would have a more subjective component and therefore more likely controversy, would be that INTENTIONAL off the ball fouls in the last 5 minutes get the new rule (either option to inbound, 2 shots and the ball, 3 shots, whatever). It would be a ref judgment call.
Another idea would be that every team at the start of the game can designate one player who, if they are fouled in the last 5 minutes, an alternative player on the team can shoot the free throws for off the ball fouls.
Regardless, i would definitely limit it to off the ball fouls. I hate the idea of coaches playing a guy who everyone knows is a bad free throw shooter and running plays where they get the ball then whining they get fouled with the ball in their hands.
Finally, in this case i do hope either nothing gets done or they start with something very small, because i dont think its really much of a problem. I dont mind rule changes in general, since its just a game designed to be entertaining, but in this case im not sure i like the idea of changing the rules to accomodate a few players' obvious flaws in their game. Every player has flaws, and teams try to exploit those. I mean, there would never be a rule that "no one is allowed to post up a player 6" shorter than themselves" or something.
In summary, i would either do no change, or i would say "in the last 5 minutes of the game, if a player is in the ref's judgment intentionally fouled off the ball OR fouled in the backcourt, then that team gets to choose 2 free throws or inbounding the ball."
I added the backcourt piece so that, for example, deandre grabs a defensive board and is immediately fouled, the clips still get to choose inbound or free throws.