I would say it's naive to think that words in English could be literally substituted with ones in German; however in a way that's something I struggle with, myself. English comes to me naturally - when I think of a concept I can generally just say it. But in German I have a concept, and more often than not - a completely empty space for how it should be expressed... I guess it's a bit different from your difficulty: I think from many years of study my brain understands the futility of - and has given up on - literally translating words from one language into another. But then I get left simply without a way to express myself... The frustrating thing is, often those useful, but unguessable expressions (like phrasal verbs), consist of the few basic words that make up the, maybe, top 100 most common words of the language, that I 100% know... like in English the combination "make up" or the German "aufgeben" (which looks like a different situation because it's written as one word, but is kind of similar, because of how it's often used, and because its cognate in English is "to give up").

A kind of random thought I just had: do you play any musical instument? Increased linguistic ability often is thought to be associated with musicality (I think it has to do with nearby or overlapping areas of the brain). I suppose if you don't you don't. I don't remember if you've mentioned if you sing along with those German songs...