Mystery solved. I've been in touch with the head of historical research at Fort Pulaski for the last few weeks who has confirmed the following, including one big suprise.
georgia flag.jpg
The above is a third bunting issue ANV battle flag, and was presented to the regiment sometime between July & August 1862. The two honours in blue are divisional, meaning that even though the First Georgia were there, they took no part in the fighting. The reverse of the flag is devoid of any battle honours. The reason you can't see this flag on display any longer is because it was put into safe storage away from Fort Pulaski due to hurricanes.
GEORGIA REGIMENTAL FLAG.jpg Georgia Regimental Flag Reverse.jpg
Now for the surprise. According to the book 'Footprints of a Regiment' the Regimental Flag (above) was only used for reviews and parades. During restoration work in 2002 however, battle damage AND blood was found to be present, so it may actually have seen some action. A smaller surprise is that the stars on the reverse are not actually white, but light blue.