It's taken more than a half year to get back to it but I finally mounted the antenna on the roof. The main problem was that the mount kit they provided was a little small for the pipes I wanted to use on the roof. I wound up buying new u-bolts and cutting my own bracket plates to make it work. It's a little hacky but so far it's stayed put. I also had to buy some longer (LMR240) cable to get to the PI in the garage.
Moving the antenna outside of the garage seems to have had a positive impact on my reception. As the coverage maps show below, I'm seeing a good distribution of planes in all directions, though I'm missing a notch towards the south. The antenna is on the north side of the house and below the top of the roof, so it's likely the roof is interfering.
I'm pretty happy with the range, though. I see a lot more planes in the 150-200mi range now, and even a handful of planes 200-250mi away (usually international flights coming in over the Pacific). Previously, I used to lose planes around Sacramento. Now they disappear around Reno.