Ask HN: How can I change my career trajectory as a PM?

Using a throwaway account here because my normal HN account uses my real name.

TL;DR: I want to upgrade my career trajectory as a product person from the ho-hum conservative company to a faster pace organization with smart people. How can I demonstrate my ambition as a job seeker?

I have about 6 years of experience in product roles, 4 years as a product owner and 2 as a product manager. My roles have been in companies that use technology extensively but don’t identify as “tech companies.” For instance, my first three years as a PO were at a major financial firm working on banking integrations and my most recent 3 years have been at a publishing company working on SaaS products that deliver the publisher’s content.

At the same time, I've launched a side project and made a couple of real B2B sales, which has been very rewarding, too. I am a self-taught programmer. I want to keep growing this side business.

I consider myself a top contributor and leader and I want to move into a more challenging product management role at a tech company because I'm frustrated by colleagues and executives that aren't very ambitious or technically skilled.

But I don't know how to switch into a PM role at a more aspirational company. The job applications are all about "how to do product" in the VC/SV sense of the discipline, which we distinctly don't do at my current company.

How can I demonstrate to potential employers that I'm the "right caliber" of PM to make this jump and get my career onto a higher trajectory?

I live in the Raleigh, NC area and cannot relocate.

Any thoughts would be appreciated.