That business about the Indian remains law, if anyone is interested, could be solved sensibly.
If remains date from within last 750 years, they are presumed Amerindian of continuing cultures and will be returned to the tribes BARRING some overwhelming public need.
If remains date from within last 1500 years, they are presumed to be of Amerindian race and will be returned to some tribes or other, again BARRING some overwhelming public need.
But, and this is key, if remains date to over 1500 years ago, they will be presumed to be of unknown race and origin, not connected with any current people, and subject to all scientific investigation as to what and who they might be.
BTW Even within the 1500 years, a suit could be brought contending the remains are European or Asian or African and (were it successful) the bones could escape the Native lockup.
Kennewick Man was almost Nordic in appearance, very Europoid.
Arguments from genes than he was "AINU" serve little purpose beyond asserting that he had come by way of Asia, eastward, not from Europe, westward.
All the Ainu label does, is kick the argument back into a discussion of who the Ainu were and where did THEY come from.
James C. Chatters (who did most of the work on Kennewick Man), in his book Ancient Encounters, says that he thinks that KM fell into the water and was washed there anyway. Probably not much to learn from the site anyway.
Maybe you should make an exception in your proposed guidelines for Minnesota: if the remains date between 600 and 1000 years old, they will be presumed to be of Scandinavian origin...