I think both of you are using the wrong metric.
I suspect that the population density in the Midwest is lower than the Northeast. More importantly, for most of the Midwest, population density has been falling for the past 100 years even though the population has been growing. If that makes you scratch your head, just realize that 80% of farm and small town children find farming and small town life to be boring and low pay. IIRC, population in South Dakota has been falling in all but 5 counties – the counties with big cities.
Which leads me to my 2 points.
First, the Midwest is not really that empty. The white man has already stolen all of the good land from the red man and has filled it up with farms. It might be sparsely populated, but the tractor has made it as productive as it can be. Adding more people won't help. Adding biotech and robots will. (And let's face it, a tractor that can drive itself is almost a robot even if there is a person in the cab.)
Second, the issue is not space. We don't want to cramp people into the empty Midwest, we want to cram them into cities. Thanks to networking effects city folk tend to be more productive. Cities also tend to be more efficient users of resources. Of course managing megacities in more complex, involving strong social structures (i.e. rule of law, not corruption), sophistication (i.e. education), and dedicated citizens (i.e. democracy).