By the way, there a a great bunch of cannons and mortars to be seen at Ft. McNair ( tons of them) in Washington DC. they had at least three 13 inch mortar barrels and one of them was recently removed by the army to go to NY somewhere. The local Govt. historian that I personally know suspects that the one removed to be the original Dictator but the Army is not forthcoming in answering questions about it. When they pulled it up off the ground the Army would not let him look at the numbers on the barrel.
Sorry Scott, but this post has nothing to do with any practical aspects of making a repro 13-incher.
The history of the "Dictator" can get complicated very easily, so I'm going to try and make this short and sweet. Edwin Olmstead (famed CW artillery historian) was convinced that a sketch of the 'Dictator' drawn by a Union Private on 7/13/1864 had the valid weight of the mortar recorded on the sheet, (17,186 lbs.) unfortunately Pvt. Herbert E. Valentine didn't leave any notes on any other numbers that were on the mortar. According to military documents only three "Army" 13-inch mortars, and two "Navy" 13-inch mortars had this same weight marked on them, and it's exremely unlikely that a U.S. Navy mortar was used in the Federal siege of Petersburg, VA.
A 13-inch M1861 mortar on a monument in Hartford, CT was for many years thought to be the Dictator, but the weight of that mortar is marked as 17,197 lbs., so now (because of the weight and some other reasons) the general consensus among historians is that this is definitely not the Dictator.
The "Army" mortar that Scott mentioned as having been moved from Ft. McNair, Washington, D.C. (where it was partially buried muzzle down in the ground) to Ft. Hamilton, in the borough of Brooklyn, New York, NY is marked with the right weight of 17,186 lbs., but because of various other facts it is not considered likely that this is the Dictator.
There are now 27 known surviving M1861 13-inch mortars, and the only one with a marked weight of 17,186 lbs. is the mortar now located at Fort Hamilton, in New York City.
In the final analysis there doesn't seem to be any certain way to know if the "Dictator" does or doesn't exist, short of some authentic documentation coming to light that has the "registry number" and/or "the foundry number" of the 13-inch mortar that bombarded Petersburg in 1864/65 recorded on it.