having worked in... a high-level functional language gives you some mental machinery that doesn't rely on decomposing this thought process into some concrete syntaxThis is what we are really talking about when we claim that reading, e.g., SICP will make you a better programmer even if you don't work in Lisp.
SICP is not a book about Scheme. It's a book about computation that happens to use Scheme. And it is resolutely abstract, encouraging you to think in non-linguistic terms. One of the bits I remember best was near the beginning, when they talk about the shapes of computational processes -- iterative processes have a different shape from recursive processes. Now I use that sort of mental picture all the time.
The goal is to think about software like a mathematician thinks about math. If you're thinking in a language, it's like the way I thought about math when I was nine years old -- to the extent that I knew what a mathematician was, I thought it was someone who was really really good at the long division algorithm. Someone who could subtract really fast!