The great stumbling block has been what to do about the West wall of the addition, where the header was partially rotted. Also, the sill on the North wall was partially rotted. The fact that the West wall header and the North wall sill had to come out was not in question. How to take them out was.
After Asha and I got the tarp pulled back and the temporary rafters (that matociquala and I put up after the last phase of heavy demo) removed, there was a lot of staring blankly at rotted wood and yours truly answering questions from his beloved with I simply don't know.
In the end, it was the electric chainsaw that broke the impasse. I cut through the 2x10 sill piece about 1/3 of the way from the East wall. With pry-bar and attitude I levered the other 2/3 up-and-out. Once that was gone, we could see that the channel in the concrete in which the sill had rested was OK. We test-fit a piece of 2x6, and that looked alright. A glimmer of hope.
With a sense that maybe, just maybe, we had found the full extent of the things that needed to be taken out, we started peeling apart the inside of the West wall. Once the old sheetrock and some other bits of wood were stripped away, we could see that quite a lot of the double 2x6 header was salvageable -- all of the rot being on the "down hill" end of the wall. We pried off a six foot chunk of header (there had been a previous repair, so this was not a single full-length piece) and then used the chainsaw to cut off a four foot chunk of the second layer of header. There was some miscellaneous breaking of things (like exterior sheathing) taking out the header pieces, but the breaking wasn't catastrophic and we finally had all of the rotten bits out!
We broke for lunch and then made a run to Home Despot for 2x10s, some 2x4s ("just in case"), some 1x6 pieces for facing, and 4x8 sheets of plywood (holy shit, we're buying decking!). The new 2x10 sill slipped right in where the old one came out. The new West wall header pieces mated in nicely (after a little more chainsaw work to notch them to fit over the sill). So, by two we had ten feet of new sill in and the West wall rebuilt.
Then came the tedious part. Starting with one not-too-rotted 2x4 rafter we saved from the demo to use as a template I started figuring out how to cut the new 2x6 rafters. There's some complex (for me) notching at both the tops and bottoms of the rafters. Asha was pulling nails and getting things cleaned up while I tried this and that. Finally, around three, I got it right. From there I started cutting new rafters. At around four we started setting them.
Of course, I was not smart enough, or prepared enough to rent a compressor and nail gun. So, we were toe-nailing these things in top and bottom. It is so much fun standing on a ladder, nailing over your head, trying to keep this rafter from drifting... Did I mention that all these things had to be toe-nailed?
By ten past five we had set all of the joists I had cut -- enough to cover a smidge over nine feet of wall, and let us put on our first piece of decking. I was dead tired. My hammer-swinging arm felt like it was going to fall off. But I was not going to quit until we had at least one piece of plywood up on that roof! And we did. With twilight upon us and time running out to get cleaned up / fed / ready for a seven o'clock meeting, we got the facer board nailed on and one -- one! -- piece of decking up and nailed.
Tomorrow's agenda -- if I can lift my arms over my head -- will be to get the rest of the decking on that section and get the tarp back in place and secured before the promised afternoon rain arrives. The East end is going to have to wait. That 1/3 of the old sill still has to come out, and we'll be into the part where the addition to the original shed joins another, later shed addition (the owners previous to the previous owners were mad, mad shed builders, and crappy carpenters to boot). I don't know if we'll get shingles on this thing this year. I'd be happy to ride out the winter with a blue tarp on the roof, as long as we get the structure rebuilt. The weather for the next few days looks wet, but the weekend has promise.
 The addition is built into a hill, the low side of the roof is the North wall, so the rafters sit on the foundation sill; the concrete block foundation come up to knee-level above the ground.