I know it can be difficult to find a T who is well versed in DID. It's not a dx that the multitude of people have so finding one is hard.
Many T's wouldn't turn away someone with DID, but if it's not something they are comfortable in dealing with because they have not had enough experience with it in their practice, I personally would be thankful that they were upfront and honest about it. I would hate to think, going into a relationship with a T only to find out they have no clue about DID, how difficult things would be then. Of course there are many T's who deal well with PTSD, anxiety and some forms of dissociation.
I hope you can find someone soon who your insurance carrier will accept. I understand your frustration over this.