Your invitation is quite surprising, given the sneering coverage of my recent newspaper editorial that you yourself posted on the Discovery Institute's website.
However, this kind of two-faced dishonesty is what the scientific community has come to expect from the creationists.
Academic debate on controversial topics is fine, but those topics need to have a basis in reality. I would not invite a creationist to a debate on campus for the same reason that I would not invite an alchemist, a flat-earther, an astrologer, a psychic, or a Holocaust revisionist. These ideas have no scientific support, and that is why they have all been discarded by credible scholars. Creationism is in the same category.
Instead of spending time on public debates, why aren't members of your institute publishing their ideas in prominent peer-reviewed journals such as Science, Nature, or the Proceedings of the National Academy of Sciences? If you want to be taken seriously by scientists and scholars, this is where you need to publish. Academic publishing is an intellectual free market, where ideas that have credible empirical support are carefully and thoroughly explored. Nothing could possibly be more exciting and electrifying to biology than scientific disproof of evolutionary theory or scientific proof of the existence of a god. That would be Nobel Prize winning work, and it would be eagerly published by any of the prominent mainstream journals. (...)
So, I hope you understand why I am declining your offer. I will wait patiently to read about the work of creationists in the pages of Nature and Science. But until it appears there, it isn't science and doesn't merit an invitation.