My first suggestion is to lay the panelling over a layer of sheetrock. The panelling, in my experience, simply is not stiff enough to support itself- unless you're putting the firring 6" apart! Nobody likes the wavy look of unsupported panelling.
(If you plan on a layer of foam insulation, the sheetrock is a MUST for fire protection. Foam burns like rocket fuel).
It is possible to use MC- it's skinnnier than pipe- but you still will have the connector running into the sheetrock, and some trimming will be needed. And then there is the issue of "mud ring" sizes.
Sure there are real shallow "cut in" boxes out there, but they will neither solve the connector problem, nor have room for more than three wires.
Wood isn't that pricey .... why not use thicker firring? A 2x2 will give you an entire 1 1/2" to work with.