I love a good mystery in my neck of the woods. I'm working on your Capt Davis by the way its a very common name and it is a bit of a slug to get through all the possibles. Working on the premise of Hawkins Island in the St Francis River, I've found an interesting tidbit that shows how a small error can be magnified in the world of the internet and auto bots.

If you do a search for Hawkins Island in Dunklin County Mo the closest fit seems to be Hawkins Lodge see:
http://missouri.hometownlocator.com/maps/feature-map,ftc,2,fid,719240,n,hawkins%20lodge.cfm

However that doesn't seem to make much sense if you look it up on Google earth nothing is there except maybe a grain bin or barn. USGS lists it as a locale not a structure. So working backwards through the old Topo maps lo and behold between 1955 and today, what in 1935 was listed as Hawkins Landing (LDG) got changed to Hawkins Lodge. A landing on the river makes more sense as a locale. The '35 map was done before all the drainage and levees were finished in the area and there is indicated the 1848 stream bed of the river with an island formed from the meander of the river between 1848 and 1935. Its not definitive but appears to be the closest fit to the info at hand. This location is just east of present day Kennett which was not much in 1860's compared to the larger more well documented Clarkton. For the 1935 map click here and you can make the present day comparison relatively easy. http://exhibits.slpl.org/maps/data/dm240007270.asp

Using this a starting point there is about five different Davis men that hail from Independence Twsp Dunklin County in the 1860 census.

FWIW
John R