Damon, I've been down a lot of rabbit-holes trying to research Adams' regiment. This is my latest attempt --

Co. A--Capt. Larkin Bunch (Newton County).
Co. B--Capt. Owens (Carroll County).
Co. C--Capt. H. L. Smith (Carroll County).
Co. D--Capt. ??
Co. E--Capt. J. W. Bishop (Carroll County).
Co. F--Capt. H. M. Moore (Madison County).
Co. G--Capt. Berry (Madison County).
Co. H--Capt. ??
Co. I--Capt. ??
Co. K--Capt. ??

Co. ??--Capt. Hiram H. Combs
Co. ??--Capt. Howard
Co. ??--Capt. John Parks
Co. ??--Capt. Samuel Phillips.

For a time, Capt. Elbert Dawson's company looked like a good candidate, but further research led me to the conclusion that Dawson's company was actually part of Chew's Arkansas Battalion.