I'm not from SD, and don't know anyone there you could hunt on.
But am curious what caliber you hunt with? Brother and I made several trips out to western Ks. (Elkhart area) and did a lot of shooting with our 17HMRs. I always wanted to take a camper out there and stay in it and hunt. We stayed in motels at night and had to drive quite a few miles to shoot.
Since then our "source" has passed away, we also was told that a lot of the farmers like to let the hunters get the dogs down to small numbers and then they go in and gas them.
Funny thing, I had just come back from vacation trip in SD and had seen those big dogs right up by the road and stuff. Then I got back and went on our first dog hunt there in Ks. Let me tell ya, the Ks dogs are less than half the size of the SD dogs. The ones up there looked like wood chucks!
Good luck if you get to shoot....jdadoug.