Im building a cave right now also. I am using Wire screen as opposed to chicken wire and shooting it with tigerfoam.
I think the chicken wire works best with burlap and plaster. you mix a wheel barrow full of thin plaster and dip sheets of burlap into it, then apply them to the frame. If you can put them on the outside first (so they are not fighting gravity) then you can spray plaster with a texture hopper from the inside.
Since you are so far along already I hope this helped a little.