I disagree with this. I've been offered jobs through blind applications several times; in fact, I've taken (some of) said jobs. I am not a senior developer; I'm about the same age as the OP.
The trick is to understand the criteria used to weed out people who apply through these venues. All you need to do, in many cases, is get to the first stage of actual interviews and let your real skills drive from there. To do this, you have to present a resume, cover letter, etc. that align more or less exactly with what the job description requires.
HR will ignore a "generalist" resume that has some but not all of the relevant skills listed and a whole bunch of other, irrelevant stuff; they'll also discard personal statements/cover letters that don't seem specific. All that's required to stand out in these cases is some limited personalization for each company, matching up the skills they want to the ones you have.