I use a Capture Clip and Leash from Peak Designs. The capture clip is on my harness, and I can just slide the camera into and out of it, locking it where necessary. This lets you free up both hands to ascend/descend the rope or climb etc, and also gives you a solid hands free platform to change lenses.
To protect the camera while it's out of the clip and in my hands, I have a Leash which is the compatible camera strap, using it in the leash configuration, attached to the capture clip - so if the worst happens and I drop it, int won't hit the floor (you can adjust how long it is if necessary).
I was looking for a good solution for taking my camera up the wall, and this works really well for me.
https://peakdesignltd.com
Then if I'm taking up another bag with lenses/whatever it will be clipped onto my harness with another crab/sling/etc as you'd expect...