The plan is good. I would use 1/2" plywood with 2 layers of Durock NexGen to raise the hearth R value. The wall shield plan is good. Be sure to leave a 1" gap at the bottom and open at the top so that air can freely convect behind the panels. Personally I am not too worried about the strips or screws behind the stove. It is a pinprick of heat and the tile on top will diffuse any direct heat.
I am also wondering the minimum distance my wood stove can be to the wall wit durock and stone wall ?
The specs for the papa bear stove say 30 inches. The stove is 24 inches and then 17 inche pad in front of the stove. That really pushes the stove and pad way out into the room.
Any advice on how I can get the stove closer to the wall?