First off, your state does not guarantee a single NR LQ permit for any species, its UP TO 10%.
Secondly federal land holdings have nothing to do with the number of available tags or permits. Its up to the State to decide how many they want for themselves and how many they want for NR's, since they hold the public wildlife assets in trust for the citizens of Montana.
What you're recommending can be done, totally eliminate LQ tags for NR's. It would require legislation more than likely, and at the least you would have get the commission to take action (not sure how your statute's and/or regulations are written). WY tag allocations are not specific to the number that NR's must be allocated(with the exception of elk), only minimum percentages for Resident allocation.
Know that in many States, you would likely experience reciprocal laws to spring up, that Montana residents would not be allowed to apply for LQ tags such as elk, deer, pronghorn, sheep, moose, goat and bison in Wyoming. Matter of fact, I would probably be involved in writing such legislation if MT takes the path you're suggesting.
But, it is ultimately up to each individual state how they want to proceed with the distribution of their wildlife resources.