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When dealing with 2-edge signals, it is important to understand that the diffracted signals will not be of uniform density and quality and may actually be of various strengths and quality at any given point in space. It is a common fallacy to assume that any given convenient location will be perfect just because it might be easy to install the antenna in that spot.
In real life, it is often necessary to search for or to "probe" for an antenna location that offers a suitable compromise for the reception of all of the desired signals. That means that, when your local conditions permit you to do so safely, that the antenna's position and location may need to be adjusted, perhaps several times, in order to seek out and hopefully find a spot where everything plays nice.
As far as the tuners go, it has been demonstrated that all tuners are not created equally. Some are better at handling certain types of signal impairments while other tuners will perform better at other types of signals while failing at decoding impaired signals that another tuner handled well. Some times, it's just pot luck as to what will happen.
You shouldn't need an amp according to your signal forecast but the signal forecast cannot account for signal attenuation and impairment caused by trees or buildings, neither of which you mentioned one way or the other. However, installing a moderate gain, low noise, overload tolerant pre-amp can be done to see if it offers an improvement.
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