Since you are well enough informed to ask, you may already know that Reservations are sovereign land and as such are like being in a different country. Tribal police and the FBI are the enforcement agencies. I don't think that you will get good info from anyone except the specific reservation LEO's themselves. If you know where you will be call those particular agencies and ask the question to them. Lawyers will just be guessing unless they actually had a case in question on the specific reservations you are interested in. Each one will probably be different.
Your LEO permit under HR218 won't apply since you will be entering sovereign domains.