Katie, I read your article with a lot of empathy; congratulations on this elegant explanation! I’ve been designing experiences through the lens of wayfinding signage design for 15+ years. I’ve recently started my own practice to pursue exactly what you’re doing — and the challenge has been to help people understand what experience design is and does.
So, in a nutshell, I would say to a potential client “I help your (patients/students/guests/customers) tell better stories.” Which to me is the currency of a connected economy. In the face of bewildering information, consumers increasingly look to quiet, relevant and connected voices to make purchase decisions. Then they share those stories, which is why we’re in business.
I’m currently a member of the SEGD (Society for Experiential Graphic Design) which is working to broaden the definition of Experience Design. The Executive Director wrote an excellent blog post: https://segd.org/blog/how-might-experiential-graphic-design-embrace-design-thinking
Hope it’s helpful. Cheers.