Really enjoyed your post, unfortunately, you didn't get the position but it seems you have learned a good deal with the interview process.
What I have been hearing on all the podcasts that I follow is that when you are in the interview you should talk through your process and also ask questions and include the interviewer as you try to deliver the code. Sometimes the test that you get won't have a quick solution and what the interviewer wants to see is how you react to pressure and if you are a good fit for the team.
I think being a self-taught coder makes things harder, we are used to having no one to talk to and it feels awkward to do it at first, I guess practice could help with that. One thing that could definitely help would be pair-programming so two of you could share ideas while coding.
Finally, the big 5 are very algorithm based and people that took a CS degree will always have some advantage in this scenarios. Doing exercises in sites such as codewars could perhaps prepare you for some of the questions that you might get in the whiteboard exercise.
I wish you the best of luck on your search :D
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