If you want to remove the leather from the rock here is how "I" would do it.
If possible remove the rock from the tank...if for no other reason it will close the mushrooms and give you room to work.
Find a place on the base of the leather where it attaches to the rock that shows some gap between it and the rock. If it is solid the whole way around, no matter, you just have to be a little more careful when you get started.
Basically all you are going to do is try to peel the leather like removing a piece of tape or a label from a cardboard box. Begin picking at the base where it attaches. Once you get it started ....grab a hold and pull!!
Pull gently as you do not want to rip the base (just like the label or tape it will be harder to get off if you tear it) once you get it off the rock attach it to another piece and replace it in your tank.
If the leather comes off the rock without tearing, the bottom of the stalk (that was touching the rock) will feel a lot harder and will not produce slime. The advantage here is that is will glue very well with minimal additional support from a piece of netting etc.
If the stalk does rip (be careful not to allow it to rip vertically) then you will need to use something to anchor it in addition to the glue.
If there are any pieces of the stalk left on the rock then potentially they could regrow into another leather. Given the proximity of the mushrooms and the polyp ...my guess is any remaining stalk would just melt and should be removed prior to replacing the rock back into the tank.
FWIW
SiF