Before you lose your head over this (pun intended) is there anyway of getting a real number of how many Democrats voted in the primary and just how many total votes were cast for the Democrat primary, if there was actually a challenger to McCaskill?
Now if you can come up with those numbers, run the numbers again for who would have won the race without the Democrat crossovers? Logic would say that Brunner still would have finished ahead of Steelman. Then factor in those who voted for Atkins out of defense of him in response to McCaskills ads.
To those in Missouri, you deserve what you got because of how open primaries totally screw up the works and you ill continue to have these little earthquakes until someone up there has the testicular fortitude to end this stupid political rule designed only to keep the establishment in position of power.
There is no party registration, so you would have to use self reporting. I doubt there is an accurate way to count. You go in and just ask for whatever ballot you want. In my heavily Republican county many Rs got D ballots because of a hotly contested Sheriff race. No evil intent, they just wanted a say since there is no R candidate for the office.