The part of me that likes systematic rank systems would like Sergeant First Class to be 3 chevrons and a rocker, after the precedent established by Pvt, PFC, Cpl, CFC, Sgt. Of course, that is not the right choice for your timeline which would deliberately be following longstanding military tradition over synthetic aesthetics.
Yep, I almost went the SFC route but decided against it for those reasons exactly. Also, it seems odd to need to distinguish a senior NCO as being "first class" among other senior NCOs (yes, I know SFC is a rank in the US Army...I still don't like the sound of it). To make it that far you need an impeccable record, so being "first class" is redundant. Speaking of redundancy, I didn't want to have any First Sergeant/Sergeant First Class confusion.
Does that mean that when Texas broke off from the U.S., a lot of U.S. sergeants changed their rank to First Corporal, and a lot of U.S. staff sergeants changed their rank to Sergeant? That's not going to be popular with the soldiers. But I can see dividing up the E-4 rank into E-4 and E-4.5 could be popular, since, if I'm not mistaken, there are a huge number of soldiers at that level.
The change in title might rub some the wrong way (i.e. a US Staff Sergeant assuming the equivalent role of a Texas Sergeant) but the pay and duty description would be similar and there would be more of a prestige factor of reaching sergeant. As Zippy said, the Texas system treats sergeants more like the Commonwealth nations, you don't get fast-tracked to Sgt. in 3-4 years like the US system.
By the way, I like using the U.S. general stars, since that has a lot of meaning in the popular imagination. And I like your decision to use one bar for Second Lieutenant, and two for First Lieutenant. That aligns with Confederate usage. I think it's more likely, unfortunately, that they'd copy the US system of one gold bar, then one silver bar, than two silver bars. I really like the arrows.
I seriously considered using the original Texas Republic system of starting the 2Lt with a blank tab, but this would be confusing with modern field uniforms. I didn't deliberately copy the CS system, but yes...they are basically the same idea. The arrows are a directly copy of the OTL Texas Republic ranks. Since Texas loves lone stars on everything, the US generals insignia was already a perfect match.