Ask HN: Doing whatever it takes to land your dream job.. advice?

I've worked in the telecommunications industry for 10+ years and have a niche specialty.

One of the few businesses that work in telecommunications, and my niche, have recently begun recruiting in my country. They're a USA business, I'm in the UK. A rare opportunity. I know a lot about their business and my skill set matches the job description.

I have sent my CV directly to the recruiters e-mail, applied through the formal application form and attempted to follow up with a phone call (but can't get through). I've also sent a 1 page cover letter that goes through the job description and provides insight to my suitability.

I'm worried I'm crossing the annoyance line.. Have I done to much? Will they see my enthusiasm (rightfully) as a good thing and not a sign of (wrongly) desperation? Maybe there's something more I could do?

Cheers!

tl;dr.. Dream job has come up. A rare opportunity. I have exactly the skills they're looking for, reputation (in my country) and the passion. Is there anything outside of applying and following up with a phone call I can do to stand out from the crowd?