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If it were me I'd try completely removing both the amplifier and the power supply from the circuit.
Here's why;
Your weakest station has a 48 db NM (noise margin)
Your antenna has roughly 8 db gain
A 4 way passive splitter has about 7 db loss
100' of RG-6 feedline has roughly 6 db loss
Most TV sets have noise figures of less than 10 db
That leaves 33 db NM at the TV set. (48+8-7-6-10=33 db net noise margin.)
I doubt that there is that much loss through the trees.
Whenever the net NM exceeds 20 db, there is no justification for amplification. Over-amplification creates interference that doesn't exist without amplification. In addition, the number of stations listed on the radar report with NM values greater that 40 is 17. The more stations there are; the greater the overload potential. The exact calculations can get complicated, but here's a quick rule of thumb for equal strength stations.
2 stations = +6 db; 4 stations = +12 db; 8 stations +18 db; 16 stations + 24 db. Your situation implies that your amplifier overload potential is about 24 db greater than reception of a single station.
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