Alright, here's another quick progress update. This afternoon after work, I spent another hour on the chair (and then I had to leave), and I was able to install the top fabric, trim it, and start attaching my bottom fabric (the dust cover).
Here's a shot of the top fabric before trimming it around the perimeter.
I should be done by tomorrow. I can probably finish the bottom fabric during lunch, and then I just have to attach the gimp (decorative edging) around the raw edge, and it'll be done.