The chair is complete! I tend to be overzealous in my use of staples when I re-upholster but nothing has come loose yet so maybe it's worth it?
I decided not to recover the back support piece and just opted to find a yard of fabric for the seat that would compliment the gray back. I like the way it turned out and with very little time invested I have a studio chair for $4.99! (cost of fabric) Yay!