Have fun with the grandkids, but when you get back to this project, here's what I just found:
Source: "Supplement to the Official Records" (Mississippi volume - forgot to write the precise citation). Cook's Company was formed per Special Orders No. 124, Para. 14, dated HdQrs Dept. of Alabama, Mississippi & East Louisiana, May 3, 1864. Greenville Cook was elected Captain on May 25,'64 (resigned> Nov. 10,'64), and is believed to have been formed from absentees from Co. F, First Mississippi, and some recruits. Stationed at Brookhaven, Miss. on June 26,'64. That's all there was. I can't attest the truth of this, sounds a bit like post-war clerks making some deductions, but this may be 100% o.k.