Don’t you just love rocky ground? What would life be without challenges? I was lucky enough to have rocky ground when I built my run and planted a bunch of fruit trees. I got enough good sized rocks to build a pile (I won’t grace it with the name wall) on the downslope side of my driveway to stop it from eroding out. If I had not been lucky enough to have rocky ground I’d have had to come up with something else to stop that erosion. Yeah, I was really lucky. I’m glad I was younger then.
I don’t know how big an area you are talking about. That wooden frame is a decent idea, but any wood that touches the ground needs to be either treated wood or one of those expensive woods that resists rot.
Depending in size and shape, our corner posts generally need to be pretty substantial but any intermediate posts not so much. Gate posts also need to be pretty solid.
Instead of using wood build a cinder block base and attach your posts to that. Mortar them together or concrete them in. You can build a footer all around your run or just do something where you want a post. Or just build your corner posts out of brick or cinder blocks.
Can you hire someone with the right equipment to set some posts for you?
Another option I really don’t like but maybe it will spark an idea in you, build a footer for the post, maybe make a cross out of timbers, and weight that down. Maybe you can find some rocks to pile in the cross to hold it steady. Or concrete it in place.