It's time to completely disassemble the engine. It's so full of gunk it's surprising that it runs. What's good to soak the engine parts in and clean them in? Fuel? Carb cleaner?

Denatured alcohol, available at a home improvement center near you.

Is that what it's actually called, or is it called something else at the store? I got to know before I go look.

That is what it is called. If they look at you funny whisper "diki-diki-dook-dook-peekee-peekee-bakala-bakala-bakla-breeeeee" in their ear, that is the other name for it.