I couldn't say that this Captain Vance is your Captain Vance. But I would not doubt it.
As you know very little informations has been compiled about the Arkansas Militias organization of 1860/61 prior to the War. I have only heard of 3 regiments, the 10th, the 13th, and the 24th. Were there other regiments between these numbers? I don't know I would suspect so especially since the 10th seems to be from North central Arkanas, the 13th from Central Arkansas, and the 24th from south and eastern Arkansas.
Another things is that larger counties had more than one company. For example Pulaski County had at least the Capitol Guards, The Pulaski Lancers, and the Pulaski Artillery. Jefferson county had at least 4 companies, the Jefferson Guard, the Southern Guard, the Pine Bluff Artillery, and a company cavalry. Besides that the students of the Pine Bluff Military Academy had organized a company of Zouaves in early 1861.
Even at this Colonel Donaldson McGregor, who commanding the 24th Arkansas, formed company "D" of Fagan's 1st Arkansas without assimulating any of those Jefferson County companies.