Proving that you can do the job comes from having the right skills listed on your resume and a strong explanation of your reason for switching tracks in your cover letter, plus getting the right points across during your interview. On your resume, list script coverage and any other type of story evaluation experience you’ve had during your internships or previous jobs. If you’ve never learned how to do script coverage, get someone to teach you, and read as many scripts as you can in your free time. In your cover letter, express your desire to switch tracks. During your interview, you’ll need to sound informed, and even if you don’t know everything about scripted development, show that you’re capable of learning quickly and are enthusiastic about the job. One way to do this is by developing a list of your favorite writers -- look up who wrote some of your favorite movies and TV shows and talk about them in the interview. You’ll also want to be familiar with the writers the company you are interviewing with has used in the past. Additionally, you’ll probably be asked to write sample coverage or provide script notes during the final rounds of your interview. Come in prepared to talk intelligently about what you liked and didn’t like in the script you were given, and if you have the opportunity to write it up, get someone more experienced to proofread the document for you. Organize your thoughts clearly and concisely, and most importantly, have an opinion.
Proving that you want the job requires networking and references. Make a list of companies that you're REALLY interested in, learn everything you can about them, and try to set up informational interviews with people who work there. LinkedIn can be a great resource. Also, tell everyone you know that you are looking for a job at that specific company (or a few specific companies), regardless of where they work in the industry. The best possible situation is for someone to recommend you with a message about how truly excited you are about that company. Make sure people are aware of your dream job.
Above all, don't let anyone tell you that you can't do the job -- that's just silly. If you really want the position and know you have the skills, go for it! It’s not always the easiest jump to make, but if you’re persistent, you’ll eventually land in the right place.