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If I lived where you live, I would put a 5’ tripod on the roof, with a 10’ length of chain-link-fence top rail cut so the total height above the roof was 12’. I would get a HBU11 and aim it at 313 degrees true. If I needed to feed multiple TV’s, I would use a distribution amp. From the 57’ TV fool plot I do not think a preamp is called for.
The 57’ plot has very good conditions for everything but WLYH CW, RF23. With conditions like that a small antenna will get CBS, PBS, ABC, NCB (RF 49) easily from the front. Fox is a strong signal so a small antenna should pull it in from the back. (A larger antenna would have a better front to back ratio, so it would get less signal from the back.)
I am not sure if that would work at 20’. At 20’ WHTM is a 1 edge path. The area around you has nasty multi path problems. With a strong main signal from a LOS path multi path is less of a problem. At 57’ I would expect less multi path problems than at 20’.
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