Before looking for the words for things outside logic, you still have to fill up the space inside logic. The standard contrast for 'heuristic' in mathematical contexts like operations research or optimization is 'formal'.
A formal method is derived from first principles or axioms and designed to produce a given outcome, whereas a heuristic method searches for a solution among possibilities.
For instance, the methods of geometry are not heuristic, they follow up the discoveries of heuristic methods more properly belonging to physics with a formalization of the observations into abstract mathematics.
If you are looking for a word that contrasts with both of those, you may be looking for 'hermeneutic' (or more extremely, 'Hermetic'), which identifies the processes by which one tries to find human meaning in facts and to unify a logical or scientific fact with an intuition not derived from observation.
One interesting way of looking at the interplay between finding patterns and assigning them meaning is captured by the distinction between 'logos' and 'mythos' in religious studies and in Jungian psychology.
At one point in history, systematizations like neo-Platonism and works that focussed upon unfolding intuitions, like alchemical thinking based in the Hermetic tradition were seen as part of philosophy. To a large degree, they no longer are. We have relativized our ways of looking at the patterns of human intuition and consider them only in terms of cultural history or through the domain of