I've been hunting in Missouri, as a resident, for around 4 or 5 years. As far as I know ALL tags are available over the counter.
You're right, we have lots of public lands to hunt. And bow hunters get several shelters from a lot of the gun hunting nut jobs.
I'm unfamiliar with the NE area, but I've been told it can be a monster breeding ground! I've heard good things from a friend of mine about the public land around Mark Twain, but that may be much further south than you want to go.