What to say in interviews when your experience doesn't match the job description verbatim?

What to say in interviews when your experience doesn't match the job description verbatim?

I've been looking for a new job for months without any job offers. I'm currently in a contract role that ends in two months, but I don't want to convert to full-time there. I have over a decade of copywriting experience for various brands plus two years of UX writing/content design experience at a giant tech company. I don't seem to have a problem getting the interviews, but when I speak to hiring managers, I'm wondering if I'm not convincing enough (or don't sound confident enough) when explaining my ability to do the specifics of the roles.

I was recently turned down by a potential employer because they wanted to see examples of longer user flows. I'm currently on a growth team, so the flows in my portfolio are naturally shorter. I've been turned down for copy manager roles in the past because I've never had direct reports, though I give examples of leadership experiences and behaviors. I'm worried I'll soon be rejected for another senior copywriter position that desires a candidate with extensive experience in TV and out-of-home. I've only spoken to the recruiter, but I described how in three years of early-career broadcast work I became well-versed in the process of collaborating with producers, clients and account managers, writing and presenting scripts, writing talent specs, casting talent, directing talent, advising during editing and post-production, etc.

I'm wondering if any recruiters, HR individuals and/or hiring managers can help me find better ways to address perceived inexperience during interviews with hiring managers or cross-functional panels. I'm already considering finding a career coach, and I have a list of leads. I also know about networking. But does anyone have any additional thoughts about why I could be landing interviews only to hear later that I'm rejected due to a lack of very specific experiences? I think my variety of experiences should be an asset. I know I could do these roles I'm interviewing for and do them well. I'm a very hard worker and quick learner. But it's like they need rock-solid evidence. I've offered to do copy exercises or trial runs with the potential brand and voice in mind, when not already required. What else should I do?