Wrong assumption - the majority of my on-site interviews don't even use whiteboards. They involve discussing real world problems and work experiences with me. I still do not get offers from them.
Maybe it helps to contact the company that rejected you and ask them why they rejected you. This would allow you to narrow down your weaknesses and improve these skills. I've never tried this myself, so I'm not sure how common such a request is, but it seems like a sensible thing to do.
This seems like a good interview process. If you're qualified for the position, then what part of the interview is working against you?
I can certainly work with a team and I can program at least as well as most of my peers, but interviews are difficult for me.
You could go find your nearest open-mic night and sing/play for the audience. You can read poetry or sing karaoke.
It's probably going to suck the first time you do this. However, keep doing it. Eventually, you will get more comfortable and confident. It takes lots of practice.
I did a lot of stage performances as a musician. I used to vomit before going on stage. Eventually, I got used to it. Eventually, I was able to interact with the crowd. Eventually, I got comfortable. This confidence helped with many other areas of my life. It did take work and pushing through the discomfort and fear. It was not easy.
This may work for you.
I’d be happy to do this for acquaintances near me (Cambridge, Mass.)