Yes, that should be a 3 inch CS Parrott you found at Vicksburg. All of the 20 to 30 Parrott Rifles made in the Deep South during 1861-62 were 3 inch guns. That was the Confederate Ordnance Bureau's regulation size until the summer of 1862. Most of those guns were probably lost when the North captured the Mississippi and sank the CS river fleet. All of the CS Parrott shells fired at Shiloh should be 3 inch caliber. Read the second paragraph of the Dec. 1862 letter below from Col. Wright - a master of Deep South projectile production. He guarantees that only 3 inch Parrott ammunition had been made previously in the Deep South.
The Southern ordnance people never wanted the smaller 2.9 inch Parrotts. In 1861 correspondence, they describe the 3 inch Parrott as just another form of the regulation 3 inch Rifle. Richmond inherited Virginia's thirteen 2.9 inch Parrotts and the 5,000 rounds the state had ordered to be made by Tredegar (included some Parrott bolts and a majority of those Bormann-fuzed). The South captured another seven or nine 2.9 inch Parrott Rifles at the great victory on the plains on Manassas, and additional Parrotts during the bloody spring 1862 Peninsula Campaign. That's why there have been so many 2.9 inch rounds dug in VA. But meanwhile, the only Parrott Rifles actually made by the VA foundries were of the 3 inch caliber. They reverted to, and formally adopted the 2.9 inch caliber, during summer of 1862 when the production of 20 & 30 pounder Parrotts began in Richmond. Afterwards, the authorities sent complete batteries of 2.9 inch Parrotts to the western theater and no more 3 inch Parrott were produced anywhere in the South.
The first color photo below shows the nose with the West Point style percussion fuze of the Parrott shell shown previously. To the best of my knowledge, only Federal 10 pounders used this fuze. I know some Deep South Reads employed a brass version. That was actually ordered by John Read himself when he set up some of the first CS foundries that made rifled field projectiles, but you don't see those in VA except on some of the heavy bombs.
Please read the second paragraph of the Dec. 1862 letter below. By that time, some 2.9 inch batteries should have been arriving in the west.
The last two book pages shown below are self explanitory. Both 2.9 inch Parrott shells pre-date the use of precision lathes in early 1862. Prior to that, I don't believe Tredegar lathed any of their Rifle shells. They were filed or sized on a grindstone. The second page which shows an obviously lathed shell with no dimple was likely among the 1,000 or so produced by Samson & Pae during 1861. They were the first to lathe their shells including some "long Archers" (i.e. Burtons) finished for the state of VA as early as June 1861.
Woodenhead