When you see a job through a post studio, or a motion design studio, animation studio, etc. that says "designer", that's in the realm of what you're looking for, because those studios want the skillset of a designer to fashion the boards. Most studios who want this kind of work, however, will not frequently post these jobs. They pay the day rate of a designer to create frames instead of having someone in-house do it because they either 1) are short staffed and need help immediately or 2) are looking for something exceptional, and beyond the typical limits of what their staff people are accustomed to. That means they usually need it quick, and they need it done extremely well. So most producers do their own headhunting and keep lists of go-to freelancers for these cases.
I market myself as a designer, which allows some room for things other than strictly storyboards, and that makes me more useful to studios. But I do that because my background is in design, and I'm capable of concepting, branding, visualizing, directing, etc. The way to convey that that is your strength, is to make your portfolio about that. I haven't published a reel in a long time, because I don't want to introduce myself to new studios by suggesting that I'll do a bunch of animation or production work for them. I want to set up the expectation of what our relationship will be, and if we've worked together and a project requires it, I'll bring those extra skills to the front. So, in response to reel requests, I tell them that I mostly do storyboarding and pitch work, and send a link to a flickr page.
All things being equal, it's just as easy to judge a designer as an animator. The work is there, right up front, to be seen just like anything else. But remember that although they are related disciplines, they require very different skillsets. As a designer, you're focused on ideation, branding, visual communication, typography, composition, etc. and there's not a lot of necessary overlap with production skillsets or concerns there. To be successful, it's certainly not about creating "looks", or "styles" for clients, it's about engaging the design process. So if you've been on the production end, and want to crossover into the design stage, keep in mind that the people you'll be running with and against likely have design backgrounds, laced with illustration and photography and layout and type design and storytelling and so forth, and if you want to be competitive you'll have to devote yourself to that.