It seems like you are not arguing against circular navigation in general, but specifically the navigation on songza.

Your problem with the unpredictability of the menus in the songza-style navigation could very easily be fixed by simply adding an arrow to each item that contains a submenu, just like the typical context menu.

An arrow could be added on the tip of each leaf of the songza navigation circle that uses has a submenu. The arrow would visually indicate that a menu will pop out if the mouse hovers over leaves with these arrows. This would function exactly as the arrows on the typical context menu.