I think there is something of a general misconception about Aristotle's work on logic.
Aristotle had a definite empirical outlook. For this reason, I don't believe he focused at all on his own introspective capabilities. I suspect he never considered his own logical intuition (he discussed intuition in relation to discovering scientific principles). His syllogistic, rather, was based on his observation of empirical facts.
What Aristotle did essentially was to identify a small number of forms of arguments regularly used by other people. He probably did it from reading philosophical works available to him. I suspect he benefited greatly in his effort from the extensive debate over the Paradox of the Liar that had started a few decades before him, and which must have made philosophers in particular more sensitive to the question of truth and falsity, and thereby to that of logic generally.
So, as I see it, he didn't think of his own syllogistic as an introspection-based formalisation of the laws of thought but rather as an empirical formalisation of proper argumentation as routinely practised by philosophers.
Thus, in respect of his syllogistic, Aristotle's logic was limited by the empirical evidence available to him to a small set of logical truths. Logical truths should be seen as a by-product of the "laws of thought" proper. In effect, Aristotle only thought to look at the by-product, and then only a small part of it, rather than at the source of it.
However, he also offered a definition of a syllogism that was also, if only implicitly, a definition of logical validity. It just happened that his definition was so formulated as to being completely general. As such, it applies perfectly, without any modification, to all deductively valid inferences that the logical tradition has discovered since. So, in effect, his definition should be seen as the best we have in terms of identifying a law of thought. And it has proved itself universal by standing the test of time over a period of 2,500 years.
Further, by recasting the notion of consequence as the central one in logic, modern logicians have also ipso facto shown Aristotle's definition of validity as the most important for our understanding of logic and therefore of the laws of thought.
Most people focus on his syllogistic to argue Aristotle's limitations, and rightly so. Yet, they forget to look at the concept of validity he effectively articulated, and which is still the best we have today.
Aristotle's definition of a syllogism
A syllogism is discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so. I mean by the last phrase that they produce the consequence, and by this, that no further term is required from without in order to make the consequence necessary.
Prior Analytics, Book I, Translated by A. J. Jenkinson, published by eBooks@Adelaide, The University of Adelaide Library, University of Adelaide