Good plan. My experience is that spraying with carb cleaner at the holes, in the holes, at the jets, in the jets and openings just does not clean a carb. Now that you say you saw gray matter, that requires a soak after almost TOTAL disassembly of all internal parts. There are a lot of parts to that little carb.
You can see that a good rebuilder is charging a fair price for all that effort and expertise and they use good parts.