Tied in with Camp Jackson, Radford's was quite likely one of the pre-war Missouri State Militia units (not to be confused with wartime MSM units). The pre-war militia's existence had nothing to do with the impending war or even politics. It was simply a militia organization like any other militia existing across the nation during the first half of the 1800s.
Unless somebody has found them in recent years, there are no known muster rolls on this pre-war militia, which, at the time of Camp Jackson, was controlled by the southern-supporting Missouri governor. After Camp Jackson the pre-war militia ceased to exist as the men belonging to it either dispersed home, or went on to enlist in more sharply-defined Unionist and Secessionist units.
A decade ago Jim McGhee and I had made passing comments on the pre-war militia in this thread--
Another such pre-war militia unit was the Louisiana Guards, a unit from Pike County, Missouri. As matters were deteriorating politically in the days leading up to the war one of the members of the Louisiana Guards, John Q. Burbridge, boldly pulled off the arms heist of the century that is discussed here--
Maybe somebody else out there can shed additional light on Radford's Battery. Or the pre-war militia...in all of my research, I never have been able to dig up much of anything on it.
I'd also advise that you look more in-depth into the men you have identified as having belonged to Radford's, starting with the census. Find out what counties they were from, and pull out the county histories for their places of their origins. The county histories might have the following--a discussion on the pre-war militia that might mention Radfords; and, biographical information on the men you have identified. Those old 1800s county histories were rich with biographical profiles of residents of the county. (Funny thing about those county histories--some of them were written when the counties were only a few decades old)
In addition, you might see about finding obituaries on the men you have identified. There might be details lurking there regarding Radford's.