Although, we have found more than once among the medieval authorities (Rishonim) that they ruled against the Talmudic rules. For example, Maimonides ruled like Abaye beyond the Ya'al Kegam cases—"if he did it, it is ineffective," "do not form separate factions," and others.

What is the explanation of Maimonides there, really?

Surely it means the rules were not treated as absolute across the board, just as the Talmud itself does.

I assume so. There are more examples, and not only in Maimonides. In my opinion, when they were convinced by the reasoning on one side, or when they found a contradictory Talmudic passage, they allowed themselves to rule like the other side.

I once wrote that all the rules of halakhic decision-making are instructions for what to do when we do not have our own decision. But when we have a position of our own, there is no need to resort to the rules. See, for example, my article on autonomy in relation to the rule of following the majority or treating doubt stringently.

Rabbi Michi, how can one ground a halakhic position not on the basis of rules?

With common sense. How were the rules themselves created? Reasoning usually stands on its own and is not based on a rule. And Rabbi Wittgenstein, of blessed memory—the later one—already pointed out that the illusion of acting according to rules is a facade, while what really stands behind it are intuitions (in his discussion of following a rule).