Aristotle’s defense of non-contradiction is famously circular: you can’t argue for the principle without using it. He admits this and offers only a negative demonstration. So it’s a starting assumption, not the most certain of all principles by argument.

Correct, and Aristotle would agree. His point is that a principle that cannot be argued for without being used is not thereby weak but foundational. Presupposed by all argument is the more accurate description than proven, and it is the stronger claim, since anyone who tries to deny the principle has to use it to state the denial. That is what his negative demonstration shows.