I had a GOdar and sold it finding it not even as good as a basic dipole indoors, and harder to position for omni reception.
A Godar might fit into your space outdoors well as best I can tell from your description, but I believe it is designed for indoor use. Not sure how well it would hold up outdoors, and its directionality could well be a problem.
YOu could most likely easily attach a standard indoor dipole antenna there and see how that does.
Otherwise, there may be other larger multielement omnidirectional outdoor TV/FM antennas available still that might, just might perform better, though these are probably harder to find these days than back in their heyday 40 years or so ago.
I worked at Radio Shack and Lafayette Radio for years back in the days when outdoor antennas were still popular. Getting any antenna, even a simple dipole, up high and outdoors is almost always a good idea if possible. After that, to do much better, you needed a larger directional antenna with more elements and a rotor to orient it for particular stations. I doubt much has changed since then regarding the SOTA in antenna technology, other than aesthetics and cost perhaps.