Pretty much. Gödel still technically applies in the sense that if I claim to have a reasoning system which is usually sound and complete, you can still use "th

Pretty much. Gödel still technically applies in the sense that if I claim to have a reasoning system which is usually sound and complete, you can still use "this statement has no heuristic explanation" to force an instance of my system reaching unsound conclusions, But having just this one example doesn't disprove that the system is usually sound. It just proves that the system is sometimes not sound (which is already assumed in the meaning of heuristic).