What if Eastern Canada was annexed by the USA, but British North America were the ones “Manifesting Destiny”?

Changes

 * The USA would have had a more decisive victory in the War of 1812, annexing what is now Quebec, Ontario, Newfoundland and Labrador, and the Canadian Maritimes.
 * The historical British North America would be very different:
 * Britain would have outbid the USA for the Louisiana Purchase.
 * Britain would control all of the Oregon Country.
 * Texas would have been annexed by Britain instead of the US, meaning that instead of the Mexican-American War, it would have been the Mexican-British War. British North America would still gain the OTL Mexican and Gadsden cessions.
 * Alaska, Hawaii, Mexico, Greenland, and the British Overseas Territories in North America, would all remain the same as in OTL.
 * Like how Canadian Confederation was formed IOTL, the British North America would eventually be confederated into the Dominion of Illahee (from the Chinuk Wawa word for “earth”), now known as simply Illahee.
 * Illahee would still be a Commonwealth Realm like OTL Canada.
 * Illahee would be divided into 10 provinces: British Columbia, Alberta, Saskatchewan, Manitoba, Oregon (OTL Washington State, Oregon, and Idaho), California (OTL California and Nevada), Deseret (OTL Utah and Colorado), Aztlan (OTL New Mexico and Arizona), Texas (OTL Texas and Oklahoma), and Louisiana (OTL Louisiana, Arkansas, Missouri, Kansas, Iowa, Nebraska, North Dakota, South Dakota, Minnesota, Wyoming, and Montana); and 3 territories; Yukon, Northwest Territories, and Nunavut.
 * The capital of Illahee would be in Victoria, BC, which means the provincial capital of BC would be Vancouver.
 * Vancouver would end up like OTL Toronto, Los Angeles would end up like OTL Vancouver, and Toronto would end up like OTL Los Angeles.