Mr. Smith:
Not certain what info you need. However, here goes with a little info which is probably not exactly what you want. This was not the first time a battery became a seven gun battery in the civil war. Brynes' Kentucky battery (CSA) became a seven gun battery when they captured a 6 pounder field piece. They fought at the Battle of Shiloh with five 6 pounder field pieces and two 12 pounder howitzers. They became a six gun battery aain shortly after.

The "Rifle, Bronze, 6 pdr, 3.67" bore diameter you mention is a type of rifled cannon that were probably rifled after they were cast as six pounder smoothbore field guns in 1853 by N.P. Ames in Springfield MA. They had the appearance of the M1841 six pounder field piece. It was a failed experiment in that bronze was a soft metal and after a period of field service, the rifling wore out. This was the same problem with the better known James rifles, more widely produced early in the civil war but were withdrawn when they began to lose their rifling. Any rifled bronze six pounder of 3.8" bore diameter was a James rifle, with the defect mentioned above. A few other hasty conversions also failed and were retired.
Ron