Your "entire" counter "argument relies on an assumption that thinking or consciousness is" nothing special, just an algorithm.

As to rigor, you can support your argument very simply by showing an algorithm generate consciousness. As to "thinking"... define it.

However, those that think consciousness is something special beyond an algorithm need not produce any evidence beyond consciousness itself, because they claim nothing more than a mystery and the admonition to be wary as ordinary mechanical behavior may be confused with the mystery of consciousness, e.g., the Chinese Room.

IOW, if you think consciousness is not mysterious, all you need is a theory (i.e., mechanical manifestation) and a demonstration!

The world awaits!