It seems like you are sorting out the possibilities. However, it sounds like you are probably going to end up in the US long term, in which case option 3 might actually work out well. Generally social security is a good deal for taxpayers in spite of all the criticism it gets. Of course, you're hearing that from a 67 year old with a wife who is now receiving SS at 65 while I wait for age 70. I never thought about it this way when I was a graduate student!
In fact, my wife's earnings essentially stopped once we had our twins, giving us 3.
One other comment--you will probably never be audited, but option 2 does require that you have a reasonable basis for believing you did pay more than half if you take the child deduction, and putting down your rationale on paper before you file would be a good document to show if you did get questioned about it later. There are two issues--first, did you correctly pay your tax, and second, if you didn't was it fraud. You may be incorrect or later judged incorrect, but you certainly don't want to be accused of fraud.
