Besides the units you already listed I show a C. M. Jones in these two units:
Company E(Washington County), 1ST(Ramsey's)Regiment Georgia Volunteer Infantry. Ensign C. M. Jones
Then at the end of the war I show him in the:
Georgia Militia Battalion of DeKalb County
Major J. Y. Flowers
DeKalb County Georgia Militia, 2ND Company
Capt. C. M. Jones
1ST Lieut. D. Chestnut
2ND Lieut. J. A. Miller
3RD Lieut. W. H. Cash
4TH Lieut. B. R. Bellinger