How do you get job interviewers to be more open-minded about you?

Background: I graduated in the wake of the 2007–08 financial crisis with a non-CS degree and found a local contract web developer job on Craigslist. It was at a web agency doing some fairly straightforward PHP and CMS web development. Given the circumstances, I consider myself lucky that I got a job after college after only three months. Then I did some bouncing around multiple more contract jobs, mostly back-end development, and lasting anywhere from 3 months up to 18 months. As is the feast-or-famine nature of contract work, I constantly alternate between working and unemployed job-seeker.

Currently I'm aiming for my first full-time job in over a decade and have a few concerns on how to best present myself as a strong self-learner with an interest in learning more at work. And also deal with adapting to a full-time schedule.

From 500 or so applications last year, 20-some interviews (all ending at different stages, there is no single "how far did I get" - sometimes it's 1 screening round, sometimes it's 1 screen + 3 tech rounds) and not a single offer yet. I generally want to get more feedback such as the following:

"You didn't get a couple problems right, but you have potential and we are going to give you a chance"

"We are going to give you a contract to hire to prove yourself"

"You have shown yourself to be a self-starter, so you can just learn on the job"

I am applying to junior roles as well, so the thought is that it's expected that I shouldn't be a master at anything. Why junior, though? Wasn't my first job more than 10 years ago? Well, remember that I have just been hopping back and forth between contract work and no work, almost since the beginning. It is not a typical career.

Am I limiting myself too much with only junior and mid-level FT jobs?

If I interview at SWE jobs and nearly every professional tells me, "you don't have what we consider SWE at my job" should I drop the "software engineer" and just call myself "web developer"?

I have worked a few jobs where I had the title of "software engineer" and others where I was called "web developer". But from what most SWE jobs actually expect you to do nowadays, I consider myself lacking many skills that would place me beyond just a "coder" to an "engineer". I know, I know, don't sell your skills short. But that won't stop other programmers from imposing their own standards onto you.

I apply to bog-standard mid-tier companies 95% of the time. Maybe even mid-tier is still too high a bar because of all the rejections. Strangely, though, my resume sometimes attracts FAANG recruiters, even though, again, I only make it through 1 or 2 interview rounds.