I did a few things to prove the transferable value of my experience:
1) I showed I could do the work. I did 3 conceptual smartphone projects with user personas, use cases, storyboards, design language, ID/UI concepts and accessories. I then sent them to a bunch of blogs. Gizmodo published one, core77 published the other... I then presented these in my interview along with the press coverage. Their response was "this is basically what we do"... not surprisingly I worked on 4 smart phone projects in 2 years there.
2) I didn't over present. I asked to get into the room 30 minutes early. I brought a duffle bag full of shoes, watches and other products I had worked on. Arrayed them on the table nicely and instead of presenting, I asked them what product they wanted to hear a story about. This got them engaged right away and showed how I could guide a conversation. I had 4 or 5 bullet points predetermined that I wanted to work into the conversation no matter what they picked.
3) I defended my value. One of the interviewers came in with a scowl on his face and said "oh, a shoe guy...". I quickly nipped it in the bud by saying "nope, not a shoe guy, a designer who has been working for almost 10 years on one of the most recognized global brands, creating industry leading products and experience designed for very targeted alpha users that spread down to mass. If frog design is not interested in a design leader with that kind of experience, let me know and we can end this meeting without wasting anymore of each other's time"... it was a ballsy response, but calculated. He was so set that being a "shoe guy" was not relevant that I had to shake him out of that opinion as quickly as possible. That got him in the seat with full attention. I then spent the next 45 minutes proving my statement... bu I gave him the conclusion in the opening minute of the interview.
It goes without saying, all three of those things are hard and anxiety producing. #1 requires a lot of extra work and it is always risky walking in the door and saying "I can do what you do". #2 is scary because you give up a lot of control of the presentation to make it a conversation. #3 is just scary, but no more scary than not doing it and leaving with nothing.
I should also say that I applied for that job 6 months prior and got a pretty mean rejection letter. Later that year a recruiter approached me about another job, I noticed the frog position was still open and I told the recruiter that is the job I want. He got me the interview. At the end of the process after I had negotiated the salary and signed the offer letter I let them know they had rejected me 6 months prior, and had they hired me based on that I would not have been able to negotiate as well nor would they have had to pay the recruiter.
Also note, all of these tactics (part of the strategy of proving I could do the job) were tailored to what works for me and my personality. That is not dissimilar to how I operate on a daily basis. However you prove your value, it has to be authentic to you.