As others have said, there is plenty of land out there. Don't limit yourself strictly to WIA areas. There are lots of other types of public lands to hunt, WPA's can be pretty good too a lot of times. GMA's can also be good.
You will come across some areas that are worthless, either because they've been hayed down, or trampled by too many hunters, or some other reason. You'll come across other areas that look like nobody has even hunted them yet this year and they'll be a hidden gem for you.
You don't need too many pieces of land to hunt either. If you hunt non-stop from 10am-5pm, at one hour per parcel, that only leaves 7 pieces of land to hunt the entire day. Now factor in drive time, lunch, and maybe some scouting, and you'll hunt even less.
Point being, there's a lot more public land than you think in SD. If a piece doesn't look good to hunt, then keep on driving to the next. With two guys you can get 6 birds a day, I'm sure some days you will get your 6 in a few hours, and other days you will struggle to get 2 or 3 all day. Each day is different, keep searching for land.