Ok, thanks to rustychips and CW I think we now have good photo documentation on all four mortars.
The first eight (SW) pics Cat posted definitely show the Fort Pitt Foundry 10-inch siege mortar that weighs 1940 lbs. You can see the foundry number 1620 marked above the rimbase, and U.S. marked in front of the two vent indentations. This is one of the mortars that has three elevating sockets, the other being the Cyrus Alger & Co. registry no. 1 tube.
The next seven photos (SE) that Cat posted (I think) must show the Seyfert, McManus & Co. mortar; although I can hardly make out any of the markings on the muzzle face, through the process of elimination it seems to be from that foundry. I can't see all of them in the photo, but this tube may have eleven elevating sockets, because some of the other M1861, 10-inch tubes that came from this foundry did. This mortar also seems to have a muzzle ring, if you look closely at the pics you can make out a faint line around the front of the tube, and this mortar also has double vents, but with no indentations.
While I've admired the looks of M1861 10-inch (and 8-inch) mortars since first seeing them, I haven't really given them a lot of attention, but there appear to be some unique variations on different cast iron tubes. Other than the differing number of elevating sockets on these mortars, the most interesting feature to me are the "gear teeth" found on the trunnion face of the Cyrus Alger & Co. Army registry no.1, 1862 mortar. The only reason I can think of for the hole in the center of the trunnion face and the teeth, would be for the attachment of a lever to aid in the elevation of the tube. I wonder if this feature was dropped from the design early on, because it doesn't impress me as being necessary, and it's not found on the registry no. 17 tube.
Another surprising thing to me is the number of sockets on two of the tubes. I can understand that the reason for being able to depress the barrel to that extent would be to facilitate unloading the mortar; but what would be the purpose of being able to elevate the tube to the point where the bore axis was pointing almost straight up, could it have been to load or service the piece?