For the institutions that really care about NA staus, what will matter is your tribal enrollment. Any other race/ethnicity you check won’t matter to them at all.
For the institutions that don’t particularly care, checking NA alone or along with any other race/ethnicity won’t matter at all.
Check just the NA box. Get the extra points for the institutions where it does matter. Make your parents happy. Once you on your own, feel free to check as many boxes as you like.