What else have you done besides pulling on the rod, which obviously does not work anyway because the paddle handle would do the job in that case.
If you follow the rod to the latch then move it by hand to see which way it pulls the arm when you manipulate it, you can feel where the levers try to interact with each other.
In theory, you should be able to push upward on that short stub of lever sticking out the side of the latch assembly and open the jaws.
You can see this lever in Steve's images. In the second pic (below the double pic) you can see the small lever just to the right of the drill bit. Push it away from the sliding bar and it should release. If it does not, something is really buggered and we may have to go to a Plan B if we can figure out what that is.
But try pushing the shorty lever, if you have not already. You should be able to see if if you can't feel it initially
On Broncos, I think the all-metal striker posts should not be an issue regarding a mis-matched size, like they can be on the ones with the plastic sleeves, but I suppose there is still a point at which they can become lodged together. But it sounds more like the latch is not releasing, rather than the gripper jaws too small for the striker.
Good luck. Keep trying. Let us know if you tried pushing that lever.
Oh, and the side that's not cooperating is unlocked, correct? If you don't have the buttons attached you will have to reach inside and unlock it manually by pushing up on the rod.
I know you may have done some of that already, but better to cover it twice than not at all.
Paul