Curious to hear if you’ve stopped using cover letters passed a certain point, or continue to use a tailored one for each role applying to.
But IMHO more than cover letters or anything else, talking with somebody above a recruiter is one of the best things that you can do! If you can send a message via LinkedIn or have a connection to somebody that works there, use that! If it’s posted on HN who’s hiring and the hiring manager posts his email, use that instead of applying through a career page. No matter how good your cover letter, a referral is always better!
In my company referrals are pretty much guaranteed at the very least a calls, so I’d suggest looking more into how you could get in touch with somebody at the company vs investing tons of energy in crafting the perfect cover letter.
For reference, I’m in a similar position in my career as you, about 10y of experience.
Good luck!