Glad you found the post helpful 
It sounds like you have a pretty solid background - certainly more solid than mine was. If the “tiny piece of paper” you mention is a one-page resume, I had the same issue. My advice would be to stop applying with your resume; you should include the resume as the first or second page of your portfolio and use that for all applications - even those that specifically ask for a resume. It shows that you think of yourself as a designer and want them to judge you by the quality of your work. If your portfolio showcases relevant skills and thought processes then it will probably speak louder than anything you could write (I learned that nugget of wisdom from reading similar posts on the core77 forums).