Go straight to insulin?

In the end, the tests may confirm that you are T1. That would eliminate questions, but in the end what really matters is getting appropriate treatment. And even if you get tested and don't come up as T1 (LADA), you still need proper treatment. And in my mind, fastings in the 180s and an A1c of 7.3 is not stable, it is out of control diabetes. And so I would encourage you to be your own best advocate. Yes, push to get a proper diagnosis, but also demand to treat to blood sugar goal that allows you to live a long and healthy life (that is Not an A1c of 7.3%), and push to get the proper treatment. You can read about how I started insulin and perhaps that will give you some context.