You need to sit down with an Arizona attorney familiar with university-based residency determination issues and discuss your specific facts as to how you feel you are a resident and the basis the university has for saying that you are not.
Regarding unjust enrichment, you have to have taken some action first that is shown to benefit the other party before you can state that the other party has been unjustly enriched.
Before you decide to file any sort of claim against anyone in your situation, you really do need to talk to an Arizona attorney to evaluate the merits of your situation.
Odd that you would actually BE a resident yet the school designated you a non resident; then on administrative appeal that designation is confirmed. I have to think you have inadvertently omitted some pertinent facts. You should know that most major universities are represented by top shelf law firms and their process are generally well vetted...it would be unlikely that they would declare you a nonresident if there was any strong argument to the contrary.
Concur with Attorney Kavanagh, see a local atty.
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Unjust enrichment is a dead-end, strategically unsound, and not worth considering.
If you are very sure of your position, you may want to initiate an action in the civil court for a declaration of residency. That kind of litigation is very technical and procedurally precise and you will need skilled legal counsel. Prior to taking any court action, you should step through each and every basis for the university's denial of your appeal and determination against your assertion of residency. For each and every element of the school's basis, figure out what your rebuttal is. Next, separate out the issues that involve disputed factual determinations. Now, look at what's left: that is your civil case. You need to step through this exercise because the court will not ordinarily substitute its judgment as to disputed facts if there is any reasonable factual basis for the university's determination. A court will much more readily correct errors of law and procedure.
I have read your subsequent comments to Mr. Rafter and you are already making a critical mistake common to laypersons: you are assuming that the bases of the opposition's position can be accounted for by their motives and self-interest and giving the opposing position short shrift because you know it is wrong. Even when such characterization of the opposing position is correct, it is a foolish indulgence, as skilled attorney's know. You get just a few moves in the legal arena and you must make the most of each of them. Failing to make sufficient analysis of the opposition's moves and strategies is usually fatal to your own success. Whatever the university's bases for its determination, you need to study and understand them if you have any hope of finding the flaws and developing legally adequate responses.
At the very least, given the cost of tuition to non-residents, you should invest in a consultation with an attorney as to whether you have any realistic prospect for success in reversing this determination. You should also factor into your evaluation how long it will take you to establish residency. If you can establish residency more quickly than you can litigate a result, that may be the answer.
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