And since I know Mudcat has its share of nautical enthusiasts, some info on the Mary Jane:

The Mary Jane was a bark in the canal area; in August 1869 it was noted that "Bark Mary Jane, sunk in St. Lawrence River; got up" (Marine Disasters on the Western Lakes during 1869).

Via Shipwrecks Near Chautauqua County, NY:

MARY JANE
Other names : none
Official no. : C ?
Type at loss : bark, wood, 3-mast (maybe schooner)
Build info : 1862, L. Shickluna, St. Catharines Ont.
Specs : 142x26x12, 345 t.
Date of loss : 1881, Nov 19
Place of loss : Long Point Cut, near Port Rowan, Ont.
Lake : Erie
Type of loss : storm
Loss of life : 9
Carrying : telegraph poles
Detail : Bound Port Hope. Ont. for Erie, PA., she was driven ashore by a storm and broke up. The first known of her fate was when wreckage washed ashore near Dunkirk, NY, on the 20th.
Owned by Capt. Flanagan and others of Toronto.
Ashore on Long Point in the fall of 1863 and not recovered until the following spring.
Another MARY JANE (US#90077) is shown in 1884 Merchant Vessels as "lost or otherwise out of service."

Some info on the first shipwreck in 1863, via History of the Great Lakes Vol. 2 by J.B. Mansfield (1899):

Captain McArthur was born in Edwardburg, Ontario, on July 12, 1847, son of Alexander and Barbara (Graham) McArthur. The father was born in Ireland and came to America with his parents, locating in Canada, where he met his wife. During the Canadian rebellion of 1837 he espoused the cause of the patriots, and as a volunteer partici-pated in several of the engagements with the Government troops. Some time after the close of the war he was commissioned pilot on the St. Lawrence river and sailed in the schooners Traveler, Gildersleeve, John Munn, and other vessels, retiring in 1855. Two years later he removed his family to Goderich, Ont., and purchasing a farm began to till the soil. It was in the spring of 1859 that Mr. McArthur began his lakefaring life as boy on the little standing-keel schooner Annexation, of 120 tons burden; she traded between Goderich and Montreal. The same year he served a short term in the schooner Wilson and bark Gem of Kingston. During the period between 1860 and 1864 he sailed before the mast in the barks Unadilla and Alexander, the Groton, Minnehaha, Minnie Williams, Trivola (which spring a leak off Oswego and after sailing to Kingston, sank), and bark Massillon, and as mate of the schooner Hercules. He was one of the crew of the bark Mary Jane when she went ashore on Long Point, Lake Erie, and capsized on the beach during a November gale; the entire crew remained at Port Rowan that winter.

All of this dates at least one version of the song to some time between 1862 and 1881, assuming the songwriter(s) were indeed basing the bit on the real bark of the same name.