Max, I've never learned anything about the later Mt. Howitzer carriage trunnion plates not being marked with the arsenal of manufacture, date, and serial no., but I think that the metal work of the gun carriage (early pack carriage) thought to be from the famous mountain howitzer abandoned during the second surveying expedition of John C. Frémont in January 1844, (that was dicovered sometime in 2006) was found to be stamped by Watervliet Arsenal.
Dan, even if the trunnion plate is marked (according to Matt Switlik, an American artillery historian) the stampings are usually totally obscured by successive coats of paint, and I don't think the authorities of the US Park Service would take too kindly to just anyone off the street asking if they could remove the paint to check the marks.
Terry, its possible that the whole stock trail was replaced if it cracked in 1889, but the information about the carriage and limber being original might be right there on the display, or one of the rangers on duty may be able to answer that question (oftentimes these rangers carry a storehouse of knowledge in their heads).
I'm really interested in the limber, because I don't have any photos of an original limber.