I am sorry that you have had a difficult time with therapists.
From my perspective the professionals take whatever comes from my husbands mouth as the real truth/only truth. They never questioned (out loud or to me in private) that perhaps he wasn't viewing things correctly. I don't know how many sessions one needs for the professional to see through the façade, because we never could get that far into therapy. So I wonder about the tests you mention.
I really cannot give an exact time frame, since everyone is different. Many people who have personality disorders tend to seek therapy for a side issue, such as anxiety or depression. While working through the side issues, it comes to the therapists attention that the patient has a personality disorder.
I understand your frustration, but it does take awhile for some patients to really open and up and feel comfortable. I know from my own experience at therapy, it took me a couple of months to establish a sense of trust with my psychologist. I was able to feel comfortable to open up about my core issues. Many people have a fear of a psychologist/psychiatrist thinking that they are "crazy" so there is a tendency to withhold certain things.
Also, diagnosis depends on the therapists style. As others have suggested, some therapists are evasive and tend to not diagnose patients as borderline, due to the stigma. Those therapists will focus on working on the maladaptive behaviors. Other therapists will have more of a direct approach and diagnose the patient.
Have you gone with your husband to all of his therapy sessions?
Have you directly mentioned that your husband may suffer from BPD?
I need to figure out who to go to and what to bring in advance.
My suggestion is to seek a psychiatrist/psychologist who has experience working with personality disordered individuals. Also, one that specializes in cognitive behavioral therapy (CBT), dialectical behavioral therapy (DBT), and/or psychodynamic therapy.