Wow, it's been a stressful couple weeks. I did a lot of research online about roofing and insulating, and ended up calling a couple roofers to come take a look at our problem. I really needed to get back to work and decided it'd be better to spend the money to have an expert take care of the problem.
I ended up getting a fantastic deal with a referral from one of my dive buddies (thanks Marty!). Jim Fick (& Company) reroofed the addition almost in one day; they finished up in about an hour the next day. Now we have a roof that should be leak-proof and is guaranteed for 30 years if we have a problem.
Here you can see how the water ran down the valleys, hit the tips of the shingles and then followed the top of the shingles outward. That's how we ended up with water under our eaves.
While we were at it, we moved the tube sky light away from the valley so we don't end up with problems down the road. Jim put down Ice & Water Shield on the eaves and valleys (even though he said I didn't need it), removed the metal valley flashing and did a "California cut" shingled valley instead. I'll try to post some photos of that when I'm up there tomorrow finishing up the tube sky light.
With the roof finished, I took some time to go diving today, and then came home to start digging the trench for the french drain and downspout drain.
The trencher made fairly quick work of digging. It took me about 90 minutes to do all the trenching in the back of the house, but then it was too dark to see. I'll finish up the digging tomorrow morning, then we'll start laying gravel and pipe. With any luck, this will resolve our issue with water in the crawlspace, but the crawlspace probably won't completely dry out until summer.