Here's what I did...
I didn't screw with the walls. They have insulation in them (theoretically). I just put 3/4" foam insulation board over the walls. I used 1"x2" lumber for firring -- not firring strips, but 1"x2"s (which are actually 3/4" x 1 1/2"), and then screwed cloth covered 3/8" plywood panels (recycled seat backs) to the 1"x2"s, and THEN put framing on top of that. I lost a couple of inches inside measurement, but it was EASY (relatively), and it has held up well.
There is a wiring chase that sticks out slightly at the bottom (the long wooden part at the bottom) it gives a nice architectural treatment to the thing. THAT'S how I covered up the plywood-to-wall gap that you ended up with (I had one, too.) Putting the chase down there on the floor gives you a good place to put electrical wiring and sockets.
Here's the entire process from beginning to end:
Here's the finished product: