Personally I would just identify a technical niche that is highly valued by certain industries, and specialize in that.
For example in high-frequency trading, there is a small niche developing ultra-low-latency FPGAs or ASICs for trading systems. The work in question is fairly straightforward compared to other industries, but most of the people with the right skillset tend to go to aerospace or other big user of sophisticated electrical engineering instead.
The number of positions in the relevant niche is low, but given that there are so few people, they won't care where they are, could sponsor a green card and will pay very well.
For example in high-frequency trading, there is a small niche developing ultra-low-latency FPGAs or ASICs for trading systems. The work in question is fairly straightforward compared to other industries, but most of the people with the right skillset tend to go to aerospace or other big user of sophisticated electrical engineering instead. The number of positions in the relevant niche is low, but given that there are so few people, they won't care where they are, could sponsor a green card and will pay very well.