Studying Japanese, I often resented the need to be aware of social hierarchy. By contrast, I would love to develop my directional awareness, and I think I would appreciate the discipline imposed by Kuuk Thaayorre! I naturally mentally lay places out on a grid which is much straighter in my mind than in reality. I "know" a place when my mind automatically fixes the mismatch between grid orientation and reality.
By the way, is anybody besides me ridiculously linguistically impressionable? The latest thing for me is getting my singulars and plurals mixed up, and spitting out tiny sentence fragments that can be completed from context but which sound childish in English, all because of the influence of my Korean girlfriend. I got an 800 on my verbal SATs, and this is horribly embarrassing and traumatic for me.
As far as I can tell the only non-native speaker who is actually fluent is Daniel Everett. Given that the language is the subject of a fair amount of linguistic interest because of its uniqueness, it's pretty amazing that he is the only one.
Not only that, but even with a natural aptitude for languages and desire to learn, it took him 7 years of living with them to get to that point.