My vote is Company F, 14th Louisiana Infantry
Company F is listed as the Concordia Rifles and Concordia is across the river from Natchez.
The Armstrong Guards were also Company A of the 14th La.
Date of the Flag ceremony in the newspaper article matches the dates for both Company's organization, etc.
William K. Penny was 2nd Lieut. of company F, and later Captain.
Albert S. Penny (19) was also in Co. F. I think he is your "ensign". These were the only 2 men named Penny in the regiment.
Although "Waterproof Guards" sounds vaguely familiar to me, I cannot find any other reference to a military company of that name anywhere.
(I did find some more recent newspaper articles referring to Waterproof guards, these turned to be guards on the Waterproof basketball team.)
As someone already pointed out, name changes for companies is not unknown.
I think this evidence is evidence is very strong, if not concrete.
Is there a more likely company?