As it turns out, most of the roof damage was a result of a leaky roof that had been fixed some time ago, albeit very shoddily. The fix had come a bit too late to prevent serious rotting.
Since our neighbor's had already shed the slate from their side of the porch roof and the slate on our side was in very poor condition, our decision was easy. Pull off the slate and anything rotted beneath (crossed fingers, crossed fingers...) and replace with asphalt shingles.
Here's a few pictures to show what we did:
Demolition day rolled around and we made fairly quick work of removing the slate. It's a job best done primarily with a small pry bar and your hands, working from the top down. We dedicated a significant amount of time huffing the 1/3 or so of the slate tiles that were in good condition to the garage for re-use on our slate main roof or for landscaping purposes. We found significant parts of the old planking completely disintegrated, and I fell through on one or two occasions!
Proving that TV ads do occasionally work even on those who don't have a TV in their house, I signed up for WM's "Bagster" for this project and was impressed by the amount of stuff we put in it. A few days after scheduling pickup, a large truck showed up and lifted the bag by remote control crane into the bed of the truck. I paid short of $40 for the bag and $144 for the pickup. Totally worth it.
After removing all the old sheathing, we found the beams to be in pretty good shape, save for some rotting on the tops of the wood beams as seen below. It was beyond irritating to realize that the rotting was all dated and now completely dry. The previous owners had let the roof become leaky for some time, before they finally decided to do something about it. Excited that we'd be able to sister a few 2xs and get on with the new roof...
We got held up by the middle section of the eaves shared with our neighbor. There the rotting was significant. This wasn't altogether surprising- we knew water was slipping between some broken tiles and filtering down into the eaves. We just hoped that there was something left to hold the new roof up.
In the picture below you can see a new beam we managed to wedge on the neighbor's side of the roof to prop up their sagging shingles, and then a second sistered beam on my side (the right side). In retrospect, I wish we had extended a new beam the full length of the roof for peace of mind. The reality is, however, if we keep water out by maintaining the roof, it really won't matter.
We also took a big dip out of the roof by slapping 2xs along the beams.
Here's the repair on the eaves and corner of the roof a bit further along. We put the aluminum soffit (just like the neighbor's on the right) back up once we were finished.
At the end of day 2, this is what the roof looked like.
The old roof had no true flashing. Here, we used a grinder and then tucked the flashing into the brick.
On a side note, Linden Painters finished our neighbor's house, which included portions of shared architecture. Below, the left window is our and the right window is our neighbor's. Interestingly, the neighbor's window opens into a closet, whereas in our house the closet was removed to make more space in the bedroom.