First off, I don't really think you need the USA to get Western Canada, because the USA was pretty much a superpower in OTL and even if you wanted them to be more powerful, I'm not sure Western Canada will make much of a difference in terms of power.
Secondly, here is a pretty good idea. I think you could have an alternate Civil War where the British give considerable more aid to the Confederates, and almost going to war with the USA. This causes a major anti-British backlash in the USA, and in an effort to stop British intervention, Lincoln gives the Emancipation Proclamation, and portrays the war as an anti-slavery crusade. This in turn causes an major anti-war backlash in Britain, which begins to end the aid, and the USA wins the Civil War. However, the American public is not placated, and small border incidents create another war scare in Britain and the USA. As this is 1866, the British are already facing a major upheaval in Europe, and don't want a war in the United States bogging them down. Furthermore, after the American's 'anti-slaver crusade', which the British were on the wrong side of, there is no stomach in Britain for a war with the USA. This leads to an alternate Treaty of Washington, which grants the USA the right to traverse Western Canada in order to have a land border with Alaska. As time goes on, however, more and more Americans are living in the Western region of Canada, and by the 1880's they outnumber the Canadians. In 1887, the USA buys Western Canada.