The “honest and straight” answer is that until you are granted US citizenship or the laws change, you will not be able to obtain a US license or work as an officer onboard a US flagged commercial vessel in US waters.
You can work unlicensed if that appeals to you then get your license when you get citizenship. I have sailed with several Eastern European officers who have gone that route very successfully. It is a good way to learn the culture and it avoids any issues that might come from working a contract on a foreign flag ship on your current license. There are limits (one year but close to 6 months will raise red flags) on how long you can be out of the country on your green card and running up against an immigration official who has had a bad day can jeopardize your status if returning from an extended trip abroad. None of that applies if you are working through an American union for an American company on an American ship.
Regarding the immigration issues, if you used an immigrtion lawyer to get your green card, go back and ask about working outside the country. They look very closely at intent so make sure you can show strong connections and an investment in the US.
Forget the yacht jobs. After a career as a chief engineer on merchant ships you probably won’t care much for that lifestyle even if you could get past the social and prejudicial barriers. I am an unlimited chief engineer (steam/motor/gas turbine) working as a shore superintendent for a company that manages very large yachts so that comment is not just uninformed opinion. There is much more to that advice but this isn’t the place to go into the details.
Depending on where you are, I would look at shore based maintenance firms that specialize in propulsion systems. There are many and most are based in or near the larger ports. You know the type of company I mean, they do warranty work and overhaul machinery used on the ships you sailed on. If you are a native speaker of another language than English, so much the better as most of the employees of those firms come from the same background and most seem to be European immigrants. The US just doesn’t seem to produce people with the skills those companies need, or the experience either.