I'd like to see this given a bit more structure, honestly. What occurs to me is constraining the grammar for LLM inference to ensure valid C89 (or close-to, as much can be checked without compilation), then perhaps experimentally switching to a permuter once/if a certain threshold is reached for accuracy of the decompiled function.
Eventually some or many of these attempts would, of course, fail, and require programmer intervention, but I suspect we might be surprised how far it could go.