Generally speaking, I find most doctors and psychiatrists who supposedly specialize in treating addiction actually just specialize in pushing the abstinence-only model of "treating" addiction.
I suggest you not so much frame your struggle vis a vis addiction, but a more general type of dependency. Any worthwhile psychiatrist would understand the difficulty of tapering off alprazolam only using alprazolam, and would be happy to provide something like clonazepam or diazepam. Diazepam actually isn't that hard to get prescribed, especially if you can make a case that the alprazolam isn't working for your anxiety as well (which, when you're trying to taper off alprazolam using an alprazolam taper, is not at all inaccurate).
I would basically just keep trying to see doctors in your network until you find one that is willing to work with you. It's a bitch, but short of getting your benzos on the black market for your taper, I don't see many other options other than trying to continue taping using just alprazolam (possible, just unnecessarily difficult).
Do you have someone who can help you manage your meds while you work on getting together a better tapering plan OP? Like someone who can hand you a certain amount of alprazolam per day, ideally like twice a day? That would make tapering on it a lot more practical.
The faster you try to taper off the benzos, the more uncomfortable you are going to be. I know there is a huge push to just get off them and be done with the bullshit, or at least that is the thinking, that isn't generally how it works. If it were that straight forward, you would have already successfully done so.
Taking a good look at the big picture and formulating a long term taper/detox plan is what I strongly suggest. Best wishes OP!