For example, at Arkansas Post, the Union reports claim to have capture 17 pieces of artillery, 5 piece were heavy caliber weapons from the CSS Ponchartrain, the 3 heavy guns at Fort Hindman itself and two 8" columbiads at St. Charles/ Deval's Bluff. Your deduct the 6 pieces of field artillery with the Infantry outside the Fort, that leaves 6 piece of field artillery inside the Fort. As I mentioned the diagram made of the forts defenses by the federals shows parrot guns as part of the forts compliment.
However, Hart's Dallas Arkansas battery was assigned to Garlands Texas Brigade which was outside the Fort and were possible armed with the 6 Parrot guns from Fort Washita. Garland's Brigade was some of the better armed Confederates in Arkansas in January 1863 and were in fact scheduled to be transferred east to Virginia, So you would think that the Parrot guns would be with Hart's Command because most of the other artillery pieces in the Trans-Mississippi were poor types which had been sent from the east to rearm the Trans-Mississippi army in July 1862, and would have been, and had proven to be, ineffective in the Virginia theater.
Of the 9 heavy caliber guns which came to Arkansas on the CSS Ponchartrain and Maurepas, 3 were captured at the battle of St. Charles, June '62 (two of these guns came from Fort Randolph north of Memphis as it was abandoned, and are on display at St. Charles, the 3rd was and 8 inch gun taken by the Federals from the bow of the sunked Maurepas) 5 were captured during the Arkansas Post expedition (3 at Arkansas Post and two at Deval's Bluff, one of which is still on display at the Old State House Museum, "Lady Baxter"). And one 8 inch gun mounted on the aft deck of the Maurepas has never been accounted for to my knowledge. Two of the Fort Hindman guns (Lady Baxter and one of the 9 inch guns) were recovered by the 12th Texas Cavalry from the Fort's well where the federal threw them when they left. These guns were repaired and used at Fort Pleasent. They were moved to Little Rock when Fort Pleasent was abandoned in July '63 and were intended to be refitted on the Ponchartrain, but were found in the Little Rock arsenal by Steele in September '63. Steele had these guns thrown into the Arkansas River where Woodruff found them during the Brooks Baxter conflict. They were place on the lawn of the Old State Capitol for years as Lady Baxter is still there. The 9 inch gun was moved to Arkansas Post for display in 1920, and was lost during the 1927 floods that wash Fort Hindman into the Arkansas River.