Funny you should mention it. I just sent off an e-mail to the Missouri Dept of Conservation, asking why we couldn't have a rifle season for turkeys, since the fall hunt is by deer methods anyway, and we can kill either sex, there is no reason to get them up close. I prefer calling them in close, but would be happy to shoot them with a rifle for fall season when you are basically walking the woods and flushing them or sitting in a stand. It's basically sight and stalk unless you have better luck than I, calling in the fall. And stalking close enough to a turkey for a shotgun is very tricky, unless you are sitting under their tree when the sun comes up or catch them in the trees as the sun goes down.
If you are in good turkey country you should be able to sit in a stand. But if you want to speed things up and have a rifle, stalk the field edges and catch them feeding in the fields. From experience a 17 HMR takes two shots to the body, three would be better. They leave small trails through the meat and don't tear it up much. A 223 does a better job with one shot with still little damage and a much better range. You should be able to spot a good gobbler with binoculars at 350 yds and cull him from the flock at the same range. Waiting patiently for the right shot, so you don't kill two or three is the hard part.Most of my knowledge comes from friends who hunt other states, but I have hunted oklahoma too.