Rocky,
“We say gadol hametzuve v’ose meimee sheinono metzuve- greater is one who does when he is commanded then one who volunteers. Those who serve the other members of society by serving in the army because they are commanded to by the government (and have kavana to help their fellow Jew) should be considered greater”
This reasoning is incorrect. Your statement is referring to mitzvos. One may be “obligated” by the secular state to serve in the army, though halacha does not obligate him. On the other hand, bikur cholim is a mitzva obligation, even if the secular state calls it volunteering.