To anyone considering a second language, I would recommend choosing one that is widely spoken somewhere where you can't get by with English - it will unlock a whole new part of the world for you.
You might also consider studying a non-Indo-European language. It will take more time, but the experience is the linguistic equivalent to discovering functional programming after a lifetime of seeing procedural code.
There's IE languages and IE languages. I think that, for example, a highly inflected free-word-order Slavic language may be more difficult to learn for an English speaker, and more revealing in the sense that you're referring to, than many non-IE languages.
(I know you know that, but many people here might not).
You might also consider studying a non-Indo-European language. It will take more time, but the experience is the linguistic equivalent to discovering functional programming after a lifetime of seeing procedural code.