I had the whole thing basically framed up before I started putting the wire up, I actually started putting wire up because my wife couldn't keep up with painting boards for me. I didnt actually start sandwiching until the very end, since it was sturdy enough with the just the first set of 2x4s. (I sandwiched all my hardware cloth between 2 2x4s) If you want any close up pictures of anything let me know, or I will try to help with any questions if needed, since I just finished almost the same coop. Looks like a good start.
What I was thinking...but am not familiar with this plan...but normally you would think that you would build a basic frame... then add mesh... then cover edges of mesh with trim.
That mesh may get in your way...or damaged...whilst building the rest of the framing.
If you screwed it on, I'd take it off...or at least not put any more up until your frame is complete.
Do these plans come with any instructions as to order of fabrication?