I would expect that Oliver Bosbyshell, Superintendent of the Philadelphia Mint from 1889 to 1894, was involved with the medal (struck on a double eagle), which was produced in 1891. He was one of the First Defenders, and was very active in the post-Civil War veteran organizations such as the Grand Army of the Republic. He also at one time sold a large collection of pattern coins accumulated during his earlier term as Chief Coiner, and knew which end of a coin was up, numismatically. At the very least, he'd be able to get his hands on an 1861 double eagle, and know who to approach among Philadelphia's private engravers and jewelers to have the work done.