Nic,

The records you are looking for are most likely contained in the National Archives microfilm of the units you mentioned. Look under the records of the quartermaster or company officers and you will find clues as to what weapons they carried.
For instance, prior to the Corinth reenactment a few years ago, I compiled a 30 page paper (another 14 pages of photographs)on uniforms and equipage of Confederate troops in Tupelo from May 30 to September 30, 1862, which I ended up posting on here. It was all strictly from original records with no 'suppositions' or 'best guesses' like a lot of people like to use.
In it, I mentioned looking at Quartermaster W. D. Hardeman's service record. He was QM for the 3rd LA. Infantry. The record contained documents showing ammunition that the unit was issued that he signed for. It listed...

6000 buck and ball cartridges

2000 Mississippi Rifle cartidges

2000 extra percussion caps for Mississippi Rifles

100 flints for muskets

8 ammo boxes
From that one paper you can tell that they used both smoothbore flintlocks and percussion Mississippi Rifles. The difference in the numbers of the types of ammo is showing you that they had more flintlocks than they had percussion weapons.
Looking under the records of a comapny commander in the 3rd LA. Inf. also showed me the equipment issued in June of 1862... 7 knapsacks, 28 canteens, 70 haversacks, 1 wall tent, 5 pairs of shoes and 1 month earlier... 2 axes, 1 spade, 11 mess pans, 8 camp kettles, 2 wall tents, 2 sets of wall tent poles, 3 common tents and 3 sets of common tent poles.
Due to limited time, I jotted down all this info in less than 30 minutes. The microfilm is available at the state archives and most universities.

Good hunting.

P.S. Something you won't find in the microfilm for the 14th Bttn. LA. SS. A company of the 19th LA. was regularly detached to serve with them, as atrrition had lowered their numbers. Also, at Chickamauga, lots of Springfield rifles were captured and put to use in Gibson'd Brigade. This is easily verified by checking the change in ammo size issued before and after the battle and mentioned in some letters as well.