Yes! The resume! It is very hard to explain that you are qualified on your resume and that all your experiences leading up to now is what makes you a great designer and a great asset to their company.
I like your idea of adding the resume to the portfolio. That is definitely more engaging and also puts your work out there first. I know for big companies it’s hard to apply with a portfolio because a lot of their HR recruiting happens with automated software that automatically ranks the best clients based on key wording etc. I really hate that process of hiring. It is so frustrating for job searching. I find it is much easier to try to make connections first then at least get your name out there to the hiring manager so they can at least pick your name out of 500 applicants.