DES MOINES: A side-wheeler built in Madison, Indiana in 1857. She was rated at 298 tons, had 3 boilers 44" circumference x 26 ft. long. (I haven't found a record yet of the boat's dimentions) She was appropriated by the U.S. for use as a troop and supply transport during the war. She was on the Red River in 1864. Also, on 22 November 1864, she struck and sank another steamer (KATIE) at Diamond Island on the Ohio River. Apparently she was dismantled in 1865 and her machinery went to a new steamer. (Source:Frederick Way, Jr., Way's Packet Directory, 1848-1994 Revised Edition; Ohio University Press, 1994; entry # 1512)
Earlier in the war (1861) the DES MOINES, along with the IATAN, WHITE CLOUD and WAR EAGLE, while transporting troops of the 38th Indiana Reg't helped recapture the steamer SUNSHINE from Confederate troops at Glasgow, Missouri, where they were using that boat to ferry troops across the river. (Source: Casler, Michael M., "Steamboats of the Fort Union Fur Trade An Illustrated Listing of Steamboats on the Upper Missouri River, 1831-1867"; Williston, ND; Fort Union Association, 1999)
ROBERT MOORE: A Stern-wheeler built at John Bruce's boat yard in Cinncinnati, Ohio, in 1864; rated at 238 tons. (Source: Way's Packet Directory; entry #4793) (I have looked in several resources, but haven't found any other information about this boat) Way states that the ECLIPSE exploded at Johnsonville, Tennessee on January 27, 1865, so if your ancestor witnessed that explosion while on the ROBERT MOORE, that gives you an exact location for a particular date.
TACONY (spelled TACONEY or TACOMY in some sources): A side-wheeler built at Paducah, KY in 1864, and rated at 293 tons. She sank at Fort Peck, MT, in 1870 (Source: Way's Packet Directory entry #5293) Casler (op. cit.) gives the dimensions as being 173' x 32', with a 5.5' draught.
The Des Moines was a fairly large boat (based on her rated capacity of 298 tons). Troop transport was basically "standing room only" from what I've read, so it is possible they might have moved that many men on one boat. It definitely would have been extremely crowded! Many times "non-essential" equipment was sent overland rather than aboard the boat with the troops.
Hopefully something here will be of assistance to you. If/when I find more, I will post it here.
Best regards,
Maggie