If your soil will grow soybeans, turnips and corn, it must be pretty decent. Nothing in the LC mix is any more demanding than those crops, but the inherent diversity and complementary nature of his legendary advice has been proven to an entire generation of food-plotters. I think if you look at your results, you'll realize that deer are basically going to eat what you plant. There is no "magic" bean, not even soybeans. While they're a good choice, if you have the acreage and deer density for beans to canopy, there are also other choices that are just as good. If your deer are eating beans, turnips and buckwheat, all with enthusiasm, your challenge is really to keep something growing year 'round while producing enough tonnage to keep them coming back. Those are the strongest attributes of the LC rotations.
You have a 3-acre field that was soybeans last year, which means it may have little growing there right now or it may be quickly filling up with weeds. I'd lightly disc and then broadcast oats and a red clover, with plans to terminate it in early fall for a rye+4 mix. (That is depending on what you're doing in the other plots this year.)