These men were from the 12th Cavalry. There were no exact matches in either the 19th or 21st Cavalry although each of those regiments had a "B" surname with a "T" given name (but no middle initial). There were no matches at all in the artillery, and I haven't looked at Morgan. I assumed that the mention of Parson's would most likely indicate a regimental affiliation rather than a brigade.

I'd be interested if you determine who the spoon belonged to...