Thank you kindly for the advice.
I had continued my reading last night, and was coming to the conclusion that was going to need to go with an outside antenna. Thanks for confirming my suspicions.
Here's a report at 35 feet. It looks better than the 20" report.
I was leaning towards a tripod mount, since I don't have a chimney, and the eave mounts looked a bit ugly. In that same interest in minimizing that ugliness (and minimizing the cabling run) I was hoping it would be okay to place the antenna on the back half of the roof, facing forward. I would get one of those "sloping tripods", and place it on the backwards-sloping part of the roof, up near the peak. This would place the top of the tripod roughly level with the peak of the roof, and the mast and antenna would be higher still.
Would this be okay? Is there a minimum height I need to achieve between the roof surface (peak) and the antenna? In other words, how much mast would I need?
Finally, what about lightning? My house is perched on top of a hill. Will I want to ground something?