Stan: I think I can put this one to bed!! on page 299 of a huge book entitled "Civil War" A Complete Photographic History. Published by The National Historic Society in 2000, and sold super cheap by Barnes and Nobel!!!
On page 299 there appears a photograph of the "Dictator" on a towed railroad wagon, it is clear that the mortar can be fired from the wagon as one can see the "Johnson" Bar used to adjust the two friction slides, there are 3 cannonballs stacked inside a wood frame in front of the mortar. Forward to page 837, (told you it was a big book) and you can see the mortar has now been rotated 90 degrees, and a platform has been moved into place around the mortar, which allows the gun crew access to the weapon for loading etc.
Finally, on page 51 of volume 3. Forts and Artillery, "The Photographic History of the Civil War" there is yet another photograph of the "Dictator" taken at the same location, this time with its gun crew standing round the mortar, the date being September 1, 1864.
All references to the location as being near Petersburg, how far this is from the scene of the battle for Cold Harbor I am not sure, so hopefully someone can let me know?