I'm thinking the angles you are working with are causing your difficulty unhitching; I've encountered it many times due to similar situations.
Sometimes if the grade is small it will bind on the ball but let go pretty quickly after raising the bed a little bit. Other times you have to literally move the truck (making SURE the trailer is chocked) to get the ball centered in the hole for it to let go. When the truck and trailer are on different grades you can watch the coupler and ball and see the angle changing inside the coupler as the tongue rises. As the ball pushes further back/forward due to that at some point you will have to do something to correct the front/back movement.
Like you, I've just raised it until the bed came up quite a ways and then it fell but that was not comfortable. What I ended up doing is stop setting the parking brake so the truck could move a little as the ball/coupler tried to move. I doubt I would do that on a severe incline as it seems you have. The other solution was to watch the ball and when it looked like it was going to be pushed to the front or back just barely nudge the truck front or back to release the ball after had just started to lift the bed and I knew it was hung. Don't know that there is a sure fire way to keep it from happening. I did always have Reese ball grease on the ball which helps. And did I mention CHOCK THOSE TIRES!!
Edit: as far as coupler damage, I have done that. Dropped the full weight of the tongue on the coupler but it wouldn't go over the ball. I had failed to pull the lever back and get the coupling lever/lock out of the way. Bent it slightly which I was able to fix. If you've done something like that it will cause you problems too.