Here is a review of a labor law article that has nothing to do with Indian tribes. It does, however, look at various public sector unions rather than private sector ones. The author researched two states with very different labor laws and how they affect the negotiations between the states and the public sector unions. While already we know the courts have already applied the NLRA to tribal businesses, there’s no reason a tribe can’t pass labor laws to make it look more like a public sector employee if it wanted to. Prof. Singel has already pointed out that revenues from tribal gaming and other economic operations go toward government operations, making the tribal businesses more like a public sector employee than a private one under the NLRA. I’ve been wondering for a while if it is even possible for tribes or tribal employees to be working with unions that understand the public sector (AFSCME, for example) rather than those accustomed to aggressive private sector negotiations (UAW, Teamsters). There are others who can answer this question, but I still think looking at articles like this might provide a useful way to think about solutions for tribes and unions.
ETA: A person might also look at Kaighn Smith’s book coming out next year, Labor and Employment Law in Indian Country. No spoilers, but he does discuss tribal public-sector labor relations law.