We've reached the terminus. Um, Anthony, the principle of non-contradiction is not indubitable any more than the rules of chess are indubitable. It's not indubitable because it makes no sense to talk of doubting it.
Rules are neither true nor false, and the principle of non-contradiction is a rule.
What is a matter of truth or falsity is belief such as 'The King in chess can only move one square at a time'. I might in a moment of extreme Cartesian scepticism wonder whether or not in holding that belief I might not have made a mistake. If you accepted a redefinition of indubitability as non-Cartesian absence of reasons for doubt then I would be willing to go along with you. For giving reasons is part of a practice of trying to justify a belief in a public context, and justification is often achieved in such contexts when the discussants settle upon beliefs which they might find dubitable in a Cartesian sense, but not in the sense relevant to their discussion. But I guess here you'll object to my recasting of the notion of indubitability.