It's odd to have to veto an indoor antenna when all the main stations are only 6 miles away, but you can't fight terrain. Your report suggests that there will be plenty of signal refracted over the hilltop so that you can get the channels you want. Two suggestions are the RCA-ANT769 and the AntennaCraft HBU-33. Height won't get you out of the shadows, so something simple on the side of the house pointing to the south-southeast should work.
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