Hallelujah! I've finally solved the last piece of the puzzle of Stirman's Regiment of Sharpshooters -- the origin of the mysterious Companies I and K.
Company I was Co. I, 6th Texas Cavalry, and Co. K was Co. H, 9th Texas Cavalry -- both detached from their former commands and attached to the 1st Battalion Arkansas Cavalry to bring it up to a 10-company regiment. Thanks are due to Lieut. George L. Griscom, adjutant of the 9th Texas Cavalry, for writing a sentence in his journal which led me to the answers we've been looking for.
Here's the complete list of the companies --
Stirman's Regiment Arkansas Sharpshooters—Lieut. Col. Erasmus I. Stirman.
Co. A—Capt. John R. Conlee; formerly Co. A, 1st Arkansas Battalion.
Co. B—Capt. John J. Clarke; formerly Co. B, 1st Arkansas Battalion.
Co. C—Capt. Thomas B. Brantley; formerly Co. C, 1st Arkansas Battalion.
Co. D—Capt. Larkin P. Beavert; formerly Co. D, 1st Arkansas Battalion.
Co. E—Capt. George C. Robards; formerly Co. E, 1st Arkansas Battalion.
Co. F—Capt. John G. Spivey; formerly Co. D, Williamson's Arkansas Battalion.
Co. G—Capt. James F. Stout; formerly Co. C, Williamson's Arkansas Battalion.
Co. H—Capt. William H. Catterson; formerly Co. B, 27th Texas Cavalry.
Co. I—Capt. Henry W. Bridges; formerly Co. I, 6th Texas Cavalry.
Co. K—Capt. James C. Bates; formerly Co. H, 9th Texas Cavalry.