How to convince potential employers that I won't get bored and leave in a few months because of my level of education (PhD)?

I'm someone who graduated with a PhD back in August. I've been job searching ever since November of last year for a full-time job outside of academia after I rejected a job offer for a renewable full-time lecturer position back in June 2024. In any case, I wouldn't have been able to defend my dissertation before I started in August 2024 anyway (that's when they wanted me to defend my dissertation) given I didn't graduate until August of this year.

At this point, I believe out of the around 125 applications I've sent (I lost track), I've had somewhere around 20 HR phone screenings, and around 10 interviews. I'm applying for clinical research assistant/coordinator, research assistant positions, etc. because I effectively didn't get anything out of my graduate level education at all and that's not hyperbole either. One of the major ones my advisors pointed to in the past is that I never learned how to write for an audience. So, all of my advisors had to copyedit a lot of my writing for my Master's thesis, qualifier project, and dissertation in order to have something defendable to the committee. That's also not a skill I'll need to learn for the positions I want anyway, so it's not a huge dealbreaker if I don't learn it at all.

As I've applied to positions, I'll occasionally contact lab coordinators or whoever else is regulating hiring (unless they specify no contact beforehand) if they are on the job listing at all. The first thing they'll suggest to me is to apply for postdoc positions, which are a no go since I don't have any publications for those and I don't have the capacity to do any right now. The second thing, which this post is concerned about, is that they'll think they can get use out of me, but that I'll get bored and leave in a few months.

The advice I've had so far is to address that I won't get bored in a cover letter in this case and to make it clear my long-term goal is to stick to labs in this case. There's two main issues I've come across in turn though:

1.) I got told multiple times by potential recruiters and folks who hire that no one reads cover letters at all nowadays.

2.) This is anecdotal, but it seems like they don't believe me at all. I can't get a good read on folks since I have various neurodivergent conditions (ASD level 1, ADHD-I, dysgraphia, and 3rd percentile processing speed) so I may be wrong. However, it just seems like they're skeptical in a way that can't be persuaded even if I'm telling them the truth that I'm genuinely interested in those positions and it aligns with my career goals. I did discuss this point with someone recently and I can't understand why there's an extra microscope based on my level of education since the concern of someone leaving in a couple of months can apply to anyone really.

As a brief side question too, I'm going to have a gap in my resume starting this month and it doesn't look like my role as an adjunct is going to be renewed for next semester given the last of the graduate students in my PhD program and the other ones got assigned courses (my PhD program was on the ropes when I started in 2020-2021 so they stopped admitting new students two years ago to graduate me and the others). How can I address an employment gap if no one is going to read my cover letter?