My son who is learning in Israel Shana Bet heard that Israel started a program which will allow non-citizens to do Sheirut Leumi, much like the non-citizen army program.
It seems that the program was enacted, but there is little information available about how to sign up.
He is very interested in doing this program and/or joining Magen Dovid Edom, so any insights would be helpful (feel free to PM if you have specific info and are willing to speak by phone).