Of course it's doable. I know nothing of the walk-in areas in KS, but I'm guessing that a late, late season rooster in KS is nearly as smart as one in SD, so if that's what you're used to in KS, you should be prepared for it in SD. I do know that in recent years, hunters in SD have shot 3.5 to 4 times as many roosters as in KS, & the average birds/hunter/day has been about 1.5, compared to about 0.9. And no, those stats don't include pen-reared pseudo pheasants at preserves. To me, that says a reasonably experienced hunter w/ halfway decent dog should be able to come to SD in January, hunt smart, pressured birds, & still get some opportunities.
Why Miller? I'm not an expert in the area, but it's not exactly a hot bed of public land or WIA/CREP areas. And I do know a couple people who own land in the area that have said the last couple years, bird numbers have been down up there due to drought, etc. Maybe I'm wrong. There are areas in SD with just tons of public land. I'd look at the SD Public Hunting Atlas & choose an area nearer one of those areas of the state. For my money, on average, WPAs are the most productive in January because they tend to have the most cattails. And ditches. Learn the rules for hunting rights of way & hunt ditches, particularly those that contain cattails near picked corn & near roosting cover.