First, I haven` hunted SD now for four years, but had hunted there, out of Redfield, stayed at the Wilson, for more than 30 yrs. so have some idea..
Can you and your brother walk? Maybe 5-7 miles a day? If so, walk the ditches along the back roads, next to good cover. It`s free, you can call your place to hunt, and you really don`t need a dog, tho they do come in handy. By walking the ditches, the birds are confined to the ditch..tho not always..so you can cover it very well. IME, birds tend to sit close, and can flush right under your feet. Should you drop a bird on private land, you do an unarmed retreive. My brother and I have hunted this way for years..no pressure from other hunters either.
I`ve walked for 5 minutes and filled, and I`ve walked for 8 miles, sections, and not. Depends. Hop-scotch with the truck, drop your brother at the end of a section, park at the other end, walk that section while your brother drives past and parks at the next. Tell one another which way your going.
In the morning, if the sun is out, walk West or North..you can see colors better that way, after noon, walk East and North.

Good Luck.