Just so we're clear, I refer to the "tulip head" ramrod as style characteristic of the M1855-61-63 Springfield ramrods. The "trumpet head" ramrod is characteristic of the M1842 Springfield. But, the trumpet head on a M1842 ramrod has a diameter of .556" and is 41 5/8" long. By contrast, the trumpet head ramrods observed on a few Richmonds has a diameter of .499" and is 39 5/8" long. It has a smooth curve leading up to the head, and shows no evidence of having been turned down to a smaller diameter. It seems like it was made for a .58 three band musket.
The two Richmond rifle-muskets carrying such trumpet head ramrods that I examined were both dated 1863. The Hill & Anthony Confederate Longarms & pistol book shows an 1862 Richmond with a trumpet head ramrod. The Murphy & Madaus Confederate Longarms books shows a high hump Richmond with a trumpet head ramrod.
It is possible that the trumpet head ramrod originally came with a Federal longarm, and was recycled in the Richmond armory during a period of ramrod shortages. But, I'm not aware of a Federal ramrod with that configuration.
Perhaps Richmond, or another Confederate armory, had a program to manufacture this shape ramrod. Hill & Anthony's book shows a Chapman rifle, a Cook & Brothers rifle, an H.C. Lamb & Co. rifle, a Mendenhall, Jones & Gardner rifle, a Pulaski rifle, a L.G. Sturdivant rifle, plus a J.P. Murray carbine, with trumpet head ramrods. Of course, the rifles all had barrel lengths around 33", so the Richmond ramrod would not be appropriate.
But, the point is that the trumpet head ramrod seemed to have wide use in Confederate manufactured weapons, although their production is unclear. I scanned Davies' C.S. Armory Richmond book, but did not see mention of this distinction.
Further information is welcome!