[phasetransition]

I watched non-US students and post docs battle this all through my time in graduate school. Our system here in the US is completely backwards when it comes to training, and then keeping, the world's brightest. Country of citizenship plays a role, as do soft skills that "mesh" with whatever US business culture you want to enter. If I was trying to do this, my introduction email letter would be along the lines of:

"Hi, I'm [name] and I want to work for [specific person/department] at [company]. I earned my [schooling] at [top school] and those [multiple # of years] are like gravity pulling my family to the US. [Something about returning to stay and having my baby grow up in the US]. I know that the visa process can be a pain, so let's chat about working for [company] and clearing the paperwork out of the way."

An introduction like this makes it clear that: 1. You're comfortable with colloquial English 2. You're here to stay and build 3. You have a family and aren't going to walk the aisle for a green card. 4. The visa process is one you're familiar with and will attack.

Good advice for all candidates to any job in the US, whether you are a citizen or not, is to get your resume in the hands of people that do hiring, and not human resources.