When I enclosed my oven, I needed to extend my outer arch about an inch and a half. I used a thin masonry blade on a hand grinder to cut slots in both the existing arch-face and the extension pieces to kind of lock them in place. In fact, I just bought a Casa 90 for a mobile project and intend on finishing that arch in the same way. I used Heatstop 50 for the mortar. So far, it's held up fine. No cracks.
As for the dome, I recommend 3 inches of "vermicrete" over the chicken wire and another maybe 3/4 inch of stucco over that. It also wouldn't hurt to coat with a concrete sealer if the box is not to be completed right away. The vermicrete is a 6 to 1 mixture of vermiculite and portland.