My model is a 2900 but it's the same concept and you do need to be pretty straight to the rig, as mentioned 6 degrees or so. As the angle changes the follower bearing starts to move down the track and move the head to the rear. To park my rig in it's current spot I needed to be at a pretty sharp angle so I positioned the rig and removed the two saddle pins on each side of the head and left the handle and head attached to the pin. If you look at your hitch you will see that there are horizontal pins on each side of the head which drop down into saddles with about 3/8 inch pins pointing front to rear which keep the head from lifting out of the saddles.
It wouldn't be my usual method of parking but it works. You could have the hitch slid all the way back and at a very steep angle and pull the truck away. Just lift the FW high enough to clear and drive out. Reverse the order to hitch up. I also fabricated a lock for my handle. Pulling the lever would drop the head and smash something like your foot. I wouldn't run without a locked handle and I drilled out the 2 saddle pins and installed small locks on them.