that is a pretty major departure, but I think ultimately the logistical difficulties are going to be overwhelming. They were in the Revolution and little has changed for the invader. The Americans may not have money, but they have good logistics.
The British were capable of mounting inland offensives in each war, and in this case have far superior logistics to the Americans with the best interior highway in North America in the form of the St. Lawrence. The Americans are stuck moving everything overland and it hurt their ability to wage war in 1812 quite seriously, not as seriously as the outright incompetent command issues but enough to prevent any of the invasions from having a good chance of victory.
Concentrating that 40,000 men is not easy... there is still an American army of good quality in upper New York State in 1814 (and it took 2 years to build up those British forces you are discussing). So a significant force must be left to watch them, as well as defend the British naval bases on the lakes
So reduce that force in size. The acquisition of sufficient horses, oxen and wagons will be much more difficult. They cannot be transported by sea in quantity in this era, so armies must acquire them locally or there is a severe shortage, not only for logistics, but also to move artillery or mount cavalry.
Not quite, 10,000 men would be more then sufficient to defend Canada, the US Army is a spent force by this period and after 1813 was never in a position to seriously threaten Canada and was incapable of offensive action, and the militia were hardly a factor anymore with call ups regularly failing to produce results. The concentration of perhaps 6,000 men to seize Washington and 14,000 to seize Baltimore and march inland could not be contested by a counter attack into Canada.
The acquisition of horse and wagon would be something which would need to be dealt with, but this is not an insurmountable task should the British choose to pursue such a strategy.
But still, it is less distance for an army to march over better and more developed infrastructure from Baltimore to Washington than it is from Queenston Heights to Toronto! I think it makes the task more than a tad easier.
Those will not be provided by the Americans nor will they be acquired in Baltimore or Washington. So in effect this army will find itself in the same position as Clinton was in New York. Tied to a fixed point and essentially under a land blockade in short order so that all supplies must come by sea. Which adds further the already serious cost to the British exchequer.
Not really, unless there is a truly massive army waiting outside of Baltimore nothing save scorched earth tactics and a gradual withdrawal would prevent the British from linking up with the forces in Washington and aiding their provision trough forage like all armies of the day were still doing. They would be able to take a considerable number of resources on the march to Washington.
Somehow I am skeptical of the State Governors obeying such an order given by Madison versus a demand he sue for peace.
So while a problem, not an insolvable one, and a further lesson that conquering even part of North America is really difficult.
It took the Union Army 4 years, railroads and steamboats to conquer the Confederacy, and it didn't have to move animals in large numbers by sea.
The point is that the British do not have to conquer[1] any part of America, they merely need to (in this strategy) keep up the blockade, take the capital, and by seizing Baltimore provide a corridor for supply and occupation of that area. With an army sitting on the capital and in all likelihood demands for peace in the US then it's just practical that such an operation would force an end to the war on British terms.
This is an operation the British may be able to pull off which does not require a significant change from OTL or in Europe to make plausible save in terms of strategy.
There are ways it could fail, but it would be well within the capabilities of the British to force peace with such an operation and discontent within the US at the time was such that peace would be more likely than not.
[1] I'm quibbling on conquer here but what I mean is the British do not need to seize and pacify any area any longer than it takes to force a peace treaty. If they outright tried to reconquer the region yes it would be a catastrophe, but that is not what they are (or were) trying to do in the War of 1812.