Good post.
The other end of the spectrum: I used to write code for autonomous UAVs back home (commercial and military). After completing my second degree in the US, I made it through to 90% of the interviews and selection process at the top firms that play in such applied heuristics. At that point I didn't think I was wasting my time, given my background and experience.
In the end, I was apologized to almost everywhere as they couldn't offer me a position because of my immigration status and there were existing federal restrictions limiting their hiring of foreign workers. Nonetheless, almost all those companies still e-mail me today asking whether I would take a position at their operations in my home country because there just aren't that many good people who do this kind of shit in the US.
Why, I ask?
Later, I got multiple offers from companies back home who were willing to pay 5 times as much and were either in direct competition to the folks in the U.S. or were selling them patented technologies that cost billions in licenses every year.
I think the simple solution to the H1B program is to have companies biding on slots. When people see companies are willing to pay 10-20k+/year extra to higher the highest levels of talent few are going to complain.
Also, I once worked for a body shop which cared little for talent and just wanted people to fill the spots as cheaply as possible. And unlike at that paperwork this would stop them for using H1B's.
Bidding is often not a bad idea, as it does help to uncover the "true" value. But it's not the solution to the H1B program. That solution is simply to let any and every qualified person into the country -- indeed court their attention and residence. Anything else is selfish, chauvinist myopia.
Where you looking for positions at military contractors or directly DoD work? If so, you should know that there are very strict laws on who can work in US military (and government) positions. Very often, you must be a US citizen to gain even lower level employment in sensitive military contracts. I know for a fact that not only do you have to have to be a natural American citizen (born in the United States), but you also have to have lived abroad only temporarily for a certain amount of time and lived consecutively in the US (for 10 years, I think?) to be eligible to earn the highest security clearances. Government work will probably remain the domain of US citizens, as very often its viewed as a national security risk otherwise.
Reminds me of a story of a Chinese-born scientist who was harrased by FBI for being possibly a communist. He got fed up with that and left the US to China, where he ended up playing key role in Chinese rocket program. You're in good company.
In the end, I was apologized to almost everywhere as they couldn't offer me a position because of my immigration status and there were existing federal restrictions limiting their hiring of foreign workers. Nonetheless, almost all those companies still e-mail me today asking whether I would take a position at their operations in my home country because there just aren't that many good people who do this kind of shit in the US.
Why, I ask? Later, I got multiple offers from companies back home who were willing to pay 5 times as much and were either in direct competition to the folks in the U.S. or were selling them patented technologies that cost billions in licenses every year.