Looking at the Blue Book, a Parker grade GH is the same as a 3. So if I counted up the lettered grades, a 7 is an AAH - one below an A-1 Special. "The early AAs have Whitworth barrels, the later AAs have Peerless." The grades just below AAH (like the AH, BH and CH) have Acme steel barrels.
Here's an ad for a very nice AAH Pigeon Gun. How does yours match up? Note that the factory letter states the gun came with 2 buttstocks - a straight and a pistol grip. All for $35,000.