Without tuning you would need to limit the swing of the arm which yours doesn't appear to have. You could get creative and make something its around 90-120 degrees if I remember correctly. Or just get a motor assembly from a junk yard then limits its swing.

 

Limiting the swing of the actuator arm is the only fix I know of. Takes trial and error to mimic the stock sweep during the key-on cycle.

 

I got a kit from CFT to delete mine. Just never deleted it. I've never had any overheat issues towing, yet. Also I'm in Maine and even with winter front, it takes a while to heat up. The AGS are supposed to add a tiny bit of fuel economy. The CFT kit might be what you need.

 

I have seen the kits/screws, and they all seem to rely on having the plastic surrounding that the actuator snaps into and the gear/arm that goes into the motor.

Unfortunately I do not have any of that, most of the 'broken plastic' bits were removed and are gone.

Everything is put back together now, but the ~ $400 (at the time) grill shutters were omitted when rebuilt.

 

There are a few youtube videos that might help show how to limit the arm swing.