You're all on the same page as I am ...
If you staple the Romex to the firring strip, you're in violation. If you attach it to the wall, you're barely legal - until you get to the box, where you have to get closer to the wall to enter the KO/fitting.
Conclusion: You either need a deeper wall, or a different wiring method. I don't think -please correct me - that MC has the depth requirement.
Now, there's nothing preventing the remodeler from using much slimmer firring strips - either 1x's or 'hat channels' attached directly to the bricks. In that case, you're really SOL, completely unable to legally run your wires or set your boxes. Hello Wiremold