Don't want to sound too negative but a previous poster is quite right. There are approx. 9000 US pilots pounding the streets right now, most of them highly qualified & experienced (like myself on my 7th month of unemployment!), most with multiple type ratings, some with other ICAO licenses. There is absolutely NO way anyone is going to convince the INS that a PPL is the "best qualified" & will not be taking a job from a US citizen. Let's face reality, this current downturn is the worse for 30 years - it's all about timing.
You might want to try another country like EU or the ME where they are actually hiring.
Your other option is to go for those green card lotteries advertised in USA Today & other media from time to time.
Best of luck, mate.