If you focus on the bigger tier I companies, you are getting interviews so your resume works. You are failing the interview/coding test. Do you have insight into which? Are you getting second interviews? Does the process stop after the coding test?
HR is a filter for applicants. They want to make the process easy and low-risk for the company, which is a critical part of the role... But the hiring manager needs to want you badly, to hire you... If the hiring manager is saying, "Hire rafiki6 at any cost, JUST DO IT" then HR will help you.
... but HR teams rarely go out of their way to promote a candidate aggressively to a hiring manager.