I love the complicated physics in this problem as much as the next guy, but it might be easier if you can mount something like
this rotary actuator next to the pivot point. This will also have the added benefit of providing a constant force throughout the rotation as opposed to a dynamic force with the linear actuator. Most pneumatics suppliers sell some version of this.
Disclaimer: I have not actually used one of these (because I haven't had the need) so I don't have any real world experience to say whether or not it's easier.