To my knowledge, medals such as you note were not produced during the war. However, later post war reunions you
see men wearing medals/medallions, etc.

I would expect, in such cases, that the men of the unit who had these produced, would have gotten the correct unit ID.

As to his regiment, I note that in the roster of the 7th Battalion, another Ellis in Company D, could be kin, also a minister!

Daniel George Wash. Ellis

Residence was not listed; a 35 year-old Minister.
Enlisted on 5/3/1862 as a Private.
On 5/3/1862 he mustered into "E" Co. MS 7th Battn Infantry
He was Surrendered on 5/4/1865 at Citronelle, AL
Other Information:
born 5/10/1826 in Vimville, MS
died 5/21/1910 in Meridian, MS
Buried: Rose Hill Cemetery, Meridian, MS

Sources used by Historical Data Systems, Inc.:
- Mississippi Confederate Grave Registry

........

As to the 41st Mississippi, they were at Murfreesboro, Stones River, December, 1862.