Another option for the antenna is an amplified antenna. (USD$ 50 - 100 here)
A friend has one and gets over 100 stations -- which is pretty good with the TV and antenna in the basement, 30 to 40 miles from the transmitters, and a large hill in the way!
The antenna inself is enclosed in a plastic case roughly 1 foot (30 cm) square and 1 inch (2.5cm) thick. The amplifier is in a small box that connects to the TV.
Last week, during the Solar Storms, he had poor reception and asked for help when getting only 16 stations.
No joy.
The following day he told me he got it working again! He had changed which power outlet the antenna was plugged in to. Originally it was plugged into a 15 foot (5M) extension cord from a distant outlet, and he had plugged it into the same outlet as the TV.
He went back to using the extension cord and all the stations came back.
UHF radio is
Weird! (and probably no RF filtering on the power cord)
Cheers,
Tom
p.s. maybe you could get a powered antenna and use the amplifier for your Yagi.