So, my suggestion would be to use 1/2"" if for no reason other than it's a standard construction size and it will simplify your life when you do the finish work (there's nothing worse than having to build up an 1/8"" mudbed that stays level all the way across). In fact, most of the time it will wind up getting blended and I can walk into a house and see that crap where they took shortcuts. Makes me shake my head in disappointment.

Is your house slump block or stick built? If frame are your exterior walls 2x4 or x6? Since any framing you add would not be load bearing (even on that exterior wall), you can hope for 2x6 and then use 2x4 for the fill frame to allow room for attaching the AR500. I have no idea what you would do if the house is block though. The furring strips are likely 1x2 so once you repair the door with block you would be able to add the AR500 but I don't know how you would attach the drywall, short of adding 1/4"" spacers and maybe gluing the sheetrock?

This is interesting... keep us updated on how the project goes. I've never had to blend in a material that disparate.