And the skywave relevant to Chicago would be at a very low angle.
How much higher and how far away are the mountains? Here in SE Michigan, we have a 600 foot terrain ridge 20 miles away and it acts as the practical limit for many signals, and particularly with all the new cochannel translators and new Canadian stations. People think it is much further to stations on the other side than it really is. Yes, I know it's FM, but look how the F(50,50) model would completely ignore this ridge. A model for AM skywave may similarly ignore such factors. A signal, particularly AM, can bend around obstructions, or reflect from the ionosphere, but it can't go through the earth or hills. I did also hear of an AM proof of a three tower array where the center tower was much higher, and the pattern "disappeared" and behaved nondirectionally at the distance where the top of the center tower was LOS and the two end towers were shadowed. The pattern reappeared where the higher tower also became shadowed. Just saying the AM model may not explain everything.