Dear unprincipled heron,
We are going to have to agree to disagree, because I believe military adventurism was the last motivation for the USA to invade Canada.
Instead, I believe that the primary motivation was economic.
By the mid-18th century all the arable land - East of the Appalachian Mountains was under the plow. Continually expanding population forced the 13 Colonies to look westwards for more arable land.
The 13 colonies were trying to expand westwards into the Ohio, Mississppi, Missouri and Red River Valleys.
Remember that the French and Indian Wars started when a Virginia-based surveyor named George Washjngton clashed with French traders. The French and Indian Wars sparked the Seven Years War which ended with the invasion of Quebec, followed a few years later by the American Revolutionary War, followed by the French Revolution and the Napoleonic Wars.
If the British had allowed American colonists to expand into the Ohio River Valley that would have reduced population density and political frustration. As soon as the USA started poising the Mississippi Valley, it was only logical to expand northwards (along the Red River) into what are now the Canadian Prairie Provinces. Then the Mississippi River becomes the logical export route for Canadian cereal crops and cattle.
IOW the 49th parallel is an illogical border for the Canadian Prairies. If you want to draw borders based on topography, climate, river basins or natural trade routes, then all of the inland prairies logically go to the USA.
The 49th parallel makes little sense until you reach the West Coast and realize that the 49 the parallel is just south of the mouth of the Fraser River. The primary reason that the border is drawn along the 49 th parallel is that it gives Canada a third port on the West Coast.