I came across a "J".W. Stewart in Newton County with a son named William W. who served in Company D, 39th. Regiment.

From Virgil's post below the 39th. did serve at Port Hudson.

This Willam W. Stewart had a brother and uncle both named Ben.

The family reseacher at this URL provides his service records.
http://worldconnect.rootsweb.com/cgi-bin/igm.cgi?op=GET&db=ploftin&id=I01981