We have great luck hunting public land in SD with a small group every year. But you have to be methodical about it. I find that a 10 mile day in chest high grass and cattail sloughs is harder on me than a 10 mile day hunting elk in the mtns of CO so get in shape.
I’ll probably get flamed for this but I firmly believe it. Unless you have a lab or similar flushing and retrieving breed that will stay right beside you leave them at home. I’ve had more birds busted out past the edge of shooting range by pointing dogs than I’ve ever got to shoot at. Late season birds that have been hunted won’t hunker and hold while you close the 30-40 yards to the point.
Don’t be slamming truck doors or dog boxes and for God’s sake don’t be yelling at the dogs or one another. Can’t tell you how many times I’ve seen birds flood out of a field out of range when my two deaf ass uncles start hollering at each other about this and that. Hunt them like you’re still hunting deer, ease along quietly in a zigzag pattern. Pause for 30 seconds or a minute every 40-50 yards, any birds that were going to let you walk by will get nervous and flush.
You will be more or less wasting your time hunting big 320 acre CRP fields as a whole. Hunt the thick nasty stuff, cattail sloughs, overgrown ponds, abandoned shelter belts, and low spots out away from the road in the middle of the big fields. Try to look for habitat that for whatever reason just might be a little more appealing to a bunch of cold nervous birds. The further away from the road and harder the walking the better, lots of guys are fat and lazy and won’t walk a half mile to a likely looking depression in the middle of a section.
If you shoot a rooster watch him as he goes down. If his head is up as he falls dose him again, shells are cheap and pheasants are tough. If he’s not dead when he hits the ground he’ll head out on foot and you’ll have a tough time finding him. Even if he looks like he’s stone dead going down mark the spot and don’t waste any time getting out there, I jog after every downed bird. Sometimes if they’re not dead but stunned you can get to them and ring their neck before they gather themselves to escape. Don’t be afraid to ground sluice a wounded runner either.

I don’t know how much of this you already knew but it works for me. I am nervous as a cat anytime I go with a group of more than 3-4 other guys, too many guns for me to try to keep tabs on. For my methods I prefer 1 or 2 trusted partners and we have developed a system that has worked for us over the years.

I hunted KS for a decade back when it was good, shot many limits of roosters there. I was completely blown away by the sheer number of birds when I started going to SD 5 years ago. I’ve hunted 3 days a year there since and never yet hunted a day without shooting a limit, it’s that good if you work at it. I’m planning on trying to keep the streak going this December. Good luck