I was browsing through the "Report of the Adjutant-General of Arkansas, for the period of the late rebellion, and to November 1, 1866," and found something very interesting.
The report lists quite a few men who enlisted in Arkansas Union regiments, but deserted (or, in a few cases, died) before being mustered into service. Consequently, their names were not entered on the company rolls, and are not listed in the Compiled Service Records. This is a whole new source of Arkansas Unionists that I didn't know existed.
It'll take me awhile, but I'm going to compile a list of these men, and will post it here. It looks like there's going to be at least a couple of hundred men. Ought to be a big help to some of you researchers.