If anyone cares, it turns out my problem was some combination of a bad dish alignment/installation and tree blockage. Techs came out yesterday, my wife said one was obviously a trainee but the older guy seemed very knowledgeable (and I agree based on what she told me), which is nice. I've read so many stories of clueless techs. It turned out that the tech who installed our slimline when we got the HR20 about a year ago did a crappy kludge job, clamping it badly onto a vent pipe. The tech yesterday said it was such a kludge that it could have actually fallen off the roof. Nice. In addition, one of our neighbor's trees has been growing into the LOS of the dish from that location. They verified using their signal meter that the 99 deg signal was very weak.
So after discussing it with my wife and me over the phone, they ended up moving the dish to the opposite corner of our roof, with more clearance to the trees, and also mounting it directly to the roof. I haven't gone up to look at the quality of the job they did, but we're getting all of our channels again. The only thing I'm a tiny bit nervous about is if they didn't seal the holes in the roof well, the possibility of leaks, but I asked him and he said they would caulk it and that won't happen.
I'm too lazy to record and type all of the signal strengths, but now 103(c) is in the mid-80s, 99(s) is in the mid-90s and 99(c) is in the low-mid 80s.
So I'm suspecting that we haven't gotten the 99 deg signals for a while now due to the poor alignment and neighbor's trees, but it only became a noticeable problem recently because they started moving some of the HD channels we actually watch over to that slot...?
Anyway, I'm happy that it wasn't a problem with the HR20, requiring them to replace the receive and us losing everything we have recorded.
For anyone who is interested, I did have to pay for the service call, I didn't get one of those calls from DirecTV to tell me that my signal strenghts are low like some people have reported. I had the option of paying $80 for the one-time call, or signing up for the protection plan for at least a year at $6/month and then yesterday's service call is $20. I thought it was definitely worth the extra $12 to have the protection plan for a year, so that's what we did. (Yes, I do know that there's that annoying 30-day waiting period...) Hopefully they'll get the billing right.
One more question... does anyone have any experience with having to rip the dish off to have a new roof put on the house -- any chance DirecTV will pay for the techs to come out to align the dish after the new roof is in? Will be kind of annoying to have to pay for another service call so soon, something we wouldn't have to pay for if we had cable (but it's certainly not going to make me switch).
Thanks to everyone who gave me suggestions above.