Barb, I just don't understand the need for furring strips and all that extra work. Maybe I am wrong, but if you locate the studs and "screw" the new rock to the studs directly over the old rock, why that would not be enough.
Now, if your texturing is so rigid and so peaky, then maybe the texturing needs to be knocked down a bit for a tighter fit with the new rock and the existing.
I would demand that screws be used on this project and not even ring shanked nails.
Barb, lets see what others have to say about this furring idea and its merits.
I for one think that this is not necessary and you are being "milked" for cash.