the us army/navy/airforce won't accept me as i am not a us citizen
not quite true. there are many non us citizens serving in the us military. perhaps the requirement for nursing is to be a us citizen, but generally, it is not required for many us military positions.
in fact, many non-citizens join the us military as a fast track to citizenship. a green card holder only needs to serve for 3 years before applying for citizenship. if in during a time of active hostilities, and having fought for the us military, the 3 year requirement may also be waived (along with the green card requirement).
as an aside, joining the us military to get to antarctica
is not a very good way to get there. there are very few actual military who live on the ice in the summer, even fewer get to winter over.
here is a site for the us scientific recruiter....sort of.
remember, the ongoing research on the ice is a multi-national effort. there will be more than one place to look for jobs. google is your friend!