A couple of typos in your list -- should be Rivers' (not River's), Wiggins' (not Wiggin's) and Reid's (not Ried's) batteries; and Monticello (not Moticello). Also, the designation of Drew Light Artillery was not official. It was the Monticello Light Artillery, but some postwar accounts call it the Drew Light Artillery.
There were two Arkansas batteries in Tennessee artillery organizations -- Hoadley/Parks in the 1st Tennessee Heavy Artillery and Harris/Dismukes in the 1st Tennessee Light Artillery (this battery was consolidated with a Tennessee battery before the Vicksburg campaign).
The Appeal Battery was never referred to as the "Arkansas" Appeal Battery. It was initially organized as the Memphis Appeal Battery (since the Memphis Appeal newspaper sponsored its organization), but became known simply as the Appeal Battery.
McNally's Battery and the Appeal Battery initially served east of the Mississippi, were captured at Vicksburg, and exchanged in the Trans-Mississippi.
Finally, just as a matter of interest, Reid's battery was to Rivers' battery, what the Pulaski Light Artillery was to the Weaver Light Artillery. Essentially, Reid's Fort Smith battery was mustered out of service after Wilson's Creek, then reorganized under Capt. David Provence for Confederate service as the 1st Arkansas Light Artillery.
Well, I think I've covered your questions. If my aging intellect has overlooked anything, let me know.
I'm glad to see, through your much-appreciated efforts, that the militia and volunteer forces of Arkansas are going to have a home at Wikipedia. That should be of immense help to historians and researchers.