I understand your wanting to eliminate as many variables as possible, but for the benefit of new guys reading this post, flatness is not as important as most folks think.
Remember, a perfectly lapped, flat stone, will change, some dramatically once wet, which is how you will use it.
I have read or seen where Lynn and others, that hone much more than most, have said, they only lap their stones, when new, and never again.
Enjoy.