Doing a late war impression you also can go with subdued rank insignia which became pretty common. Just sew on the lozenge (diamond part of the chevron)
The subdued rank is actually getting over-represented these days. The barometer swung too far in the other direction and I think we need to tone it down a little bit. Just got too trendy. Same with blue chevrons on CS garments.
Do what others have said and don't worry about the backing. I'm not sure if there are any original CS garments that show that type of construction. There's also so many different shades of the imported cloth that unless you know for sure what batch of fabric your jacket is from, it won't match.
Historically, evidently depended on circumstances, etc. In Larry J. Daniels' "Soldiering in the Army of Tennessee" he notes a late 1863 observation by some that Bragg's army of Tennessee had largely done away with bothering about "chevrons" at all.
I, personally, don't even bother with my rank insignia at all(corporal, I have ONE early war jacket with chevrons on it) and leave the sleeves plain. My unit knows who I am, they're a pain to sew on, and quite frankly we most times don't have enough people to justify having an officer, two sergeants, and a corporal. Plus if I go somewhere without them, I don't have to worry about it.