For a listing of EMM units (incomplete), including the 2nd EMM, click here http://civilwarstlouis.com/militia/militiaunits.htm. You can surf around the links to that site to get a better handle on the nature of the EMM.
I am just speculating, the 2nd EMM probably was not called up, en masse, for active duty, except for that one time (although it is possible that various elements of it were called up during Marmaduke's 2nd raid in 1863, or to engage in training, labor on defensive works, participate in guard duty at the prisons and public buildings, provide escorts for trains, patrol the streets, etc.) As you study your Missouri Civil War history, you will see that a very major threat was unfolding in regard to St. Louis at the time the entire 2nd EMM was called up in the fall of 1864. That threat took the form of Price's Raid, wherein a Confederate force under the command of Sterling Price had entered southeast Missouri and had St. Louis specifically targeted. On the very date that Col. Stafford was called to duty himself--Sept. 27, 1864--a major battle was taking place at Pilot Knob, 85 miles away from St. Louis (and even closer to Carondelet).
You do have your work cut out for you in regard to the spelling involving in the man you are researching. I did neglect to fully respond to your initial question with my first answer--the Missouri State Archives in Jefferson City house the muster rolls for the various Missouri units. These are oversized sheets that provide reports, company by company, of the unit's monthly activities. They list the members of the company by name, and provide personal information on each one, as well as their status as of the date of the report. The muster rolls also list a synopsis of that month's activities for the unit (which might possibly provide additional detail on where the camp was). In any event, by going down name by name, you may come across an alternative spelling for your guy.