If stay less than 35 days in the US per year, your overseas earnings are only taxed if you exceed approx $88,000/year. And even then, they can only tax the money you earn above this threshold (ie: anything made above $88,000).
If you are in the USA more than 35 days a year, than I believe they will tax your entire world wide earnings. At least that's how I understand the law.
The catch 22 for you is that in order to maintain your US Residency, you have to make it seem like you are residing in the USA. In doing so, you will have to spend more than 35 days back home which is opening you up to full taxes on your entire salary.
You will have to do the math.... the money can be good over here at times but if you're not earning tax free money at the end of the day, is it really worth it???
Good luck with it.... Be smart as you may not want to jeopardize your greencard status.
Yank.