Speaking as someone currently involved in hiring for Senior roles at my company: We have hundreds of resumes, most of which are garbage. We're not seeing a lot of evidence of large numbers of people working hard to tailor their resume to the role, so doing so would absolutely help you in our case.

Even more so, if we got a referral right now from within the company we'd absolutely skip them straight to the interviews. Dealing with resumes sucks right now as an employer, and we want to avoid that stage as much as you do.