I did have a feeling that is how it was going to work. You just can't be a Nebraska resident without a Nebraska DL. At least for now you have a work around, maybe someday it will be made right for all citizens of the US. I doubt that you will be able to get a Nebraska permit, but at least you are covered.
My father is a Texas resident, he owns more property in Nebraska than he does in Texas, but he has nearly no rights here other than paying the property taxes. At least his Texas permit is honored here.