I simply don't agree with your blanket statement that "listen and learn" does not work for adults, or that our ability to emulate language sounds is completely lost after age X.
You say yourself that immersion is not a guarantee - that in itself leaves some room for a conclusion that, for some, it works.
In the end, it seems that there is no other way but listening and repeating - we hear things, we say things, we hear other people say "do it like this", we try again, repeat as necessary. What's the alternative?
Now, I'm talking strictly about pronunciation here. I agree, the grammar and vocabulary must be learned as adults by rote memorization to a large degree, and by "listening and learning" to a much lesser degree.
At any rate, again, we're left with a description of what does not work, or what is not guaranteed to work. What does? What's the answer for those interested in improving their blas and their Gŕidhlig?