It's an interesting question. I've always viewed SDET's as the red-headed step-children within a dev organization...but I don't have a good reason for feeling this way. It's a legitimate role, and takes a lot of skill. But for some reason, when I'm on the job hunt, I never even come close to considering positions that were labeled as SDET.

I'm not sure why SDET roles leave such a bad taste in my mouth. Maybe it's because they're typically looking for junior devs, or maybe the role just feels too removed-from-the-action.

Ironically, I've worked in positions that would be considered by some to be an SDET role (I spent all day writing tests to raise the coverage on other people's untested code) ...but those roles were advertised as "Senior Software Engineer", and framed as "we need someone senior to come in and look after the code that the junior guys are writing" so I felt better about it. I guess it's all how you frame it. If you take the position that the role is less of a janitor, and more of a manager, then you might attract more senior folks.

I your particular case, I'd also add the advice to remove the coding challenge from step 1. As a senior/lead dev, I'm always up for a coding challenge during the interview process, but only after I've touched base with a real human. I'd never apply to a role that required a challenge up-front just to send in my resume. Just my 2 cents.