i was talking to tony on this but like i said rigging is not my thing i just build hulls.
i remember reading both the British and the americans never built and rigged ships for the lakes, the French were building and sailing the lakes long before both the Brits and americans so they relied on the French. By the war of 1812 everyone pretty much had figured it out.
the Niagara, the Eagle, the Oneida and the Jefferson were all designed and built by the same crews Noah Brown and Henry Eckford. They rigged the ships for the Great Lakes. So using these ships as a reference will get you very close to how the Oneida was rigged. Once they figured it out all the lakes ships were about the same in masting and rigging
i am not very knowledgeable on rigging