A couple of pieces for the puzzle..

In April 1863, there is a reference to Brown's Battery of Greene's Brigade in Holmes' General Order No.10. This refers to the court martial of one of the battery's soldiers for offences committed in February 1863 when the battery was stationed at Batesville, Arkansas
(link - http://babel.hathitrust.org/cgi/pt?id=dul1.ark:/13960/t7xk9457n#page/n1/mode/1up)

OR Vol.22, Part 2, p.846 shows the battery in Greene's Brigade as of 20 May 1863, with the added comment "ordered to Little Rock".