I have the Godar which works well. It costs about $50. It is directional but does a decent job pulling in other stations not in its line.
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.
I use the Magnum Dynalab ST-1 vertical FM antenna and have for the past 4 years. It is mounted high on my roof and I live 50 miles away from any good FM station. It has great reception and is durable. If you could spring for $114 the Magnum is a great option. Being a single stiff wire it is unobtrusive and easy to hide and has a coax connection. They also sell the indoor SR-100 which I have not tried but MD makes many good antennas and has a good reputation.
I also own the MD ST-2 and was wondering if I couldn't connect it to my MFJ -901B. The MFJ 901B is a Versa Tuner box with knobs for Antenna, Inductance and Transmitter. You could possibly just buy one of these boxes, connect it to the tuner and run your own copper wire around the inside of your attic. There is a ground connection on the back of the box. Does anyone know about the MFJ?
Here is their website;
I've used the indoor antenna from Lake and consider it the second best indoor antenna. First is the Ccrane FM Reflect dipole which gave me greater signal strength and positioning flexibility. I have also tried one of those Radio Shack amplified antennas and it did nothing but amplify noise. I returned it.