It must be difficult to be turned down for telling the truth but I think it is good that you are upfront. If they can't deal with your issues why wait and risk rejection later.

I think DBT would be great for helping you develop the skills to deal with your attachment issues. I know it can be difficult to find one that takes insurance but keep looking and at least get your name on the waiting list. I was lucky enough to come across one that only cost $35 a week.

I would also recommend looking for a T that uses DBT as one of their modalities. Thwy will probably be more accepting and able to work with your issues and usually have contacts to help you get your foot in the door for a DBT class. Many will teach the classes themselves and many DBT classes will require you to see a T linked to their program.

DBT classes also provide outside coaching contact with the T or facilitator to help you through those times when you are dealing with urges. I don't have attachment issues but I have gained a lot of emotional regulation coping techniques through DBT classes.

Keep looking and don't give up on yourself. The right match is out there. Just have patience.