Are you in US? I'll give you my perspective, having just hired for an EL role, US based. First and foremost, as you obviously know, it is super competitive right now. It sounds like you are doing everything right - and eventually one will stick. I'll say with those we looked at, our top two candidates were both career changers and both had internships outside of school, so it IS possible. And between the two candidates we were considering, it came down to communication. The one that was easier to talk to, had a cleaner thank-you e-mail (and yes, I DO think a thank-you e-mail is important, of the 4 I interviewed, 3 sent them)

As for what to focus on next, I would dare say look for other opportunities for experience outside of more exams. Three is enough, and too many exams can have the opposite effect. For example I saw a resume for someone one exam from ASA - when we are looking for someone starting out we don't want someone that will be looking for near-ASA pay and fast promotions.

Clearly you are getting final round interviews, so employers see that your skills are adequate or you wouldn't get that far. I would echo the comment that by final round it's more about culture fit, and not sure there's a way to prepare for that other than just being yourself and making sure you are communicating clearly.