Napoleon only needs to open up for a month, then he can get his men and enough supplies to last awhile. In OTL, the British Mediterranean fleet was larger than the Home Fleet in guns, tonnage, and ships and the Mediterranean fleet could be called for the evacuation if they have a TPK at Trafalgar. Although if they lose Trafalgar, the better move is ask the Mediterranean squad to replace the home fleet and secure the channel to block a crossing.
Napoleon not EVER being able to ship an army across the Channel wasen't what I was critiqueing: I'm hardly one to buy into the myth that "Britannia Rules the Waves" is an ironclad fact of history (Though, you do need the second half of that statement to be true for the first half to also be so: Britain can't be a superpower without firm control of her home waters). Rather, it was two other points one of which you covered yourself.
A) Priorities. The British Mediterranean forces, if they still exist in large enough quantities to stage a successful evacuation of what would be needed to set up the pre-requesit position in Canada to not only fend off the French and Americans, establish firm control over the region's native and French Canadian majority, and stage a successful conquest of New England, than they would quickly move to replace the home fleet and cut Napoleon's army off from the Continent to choke it of reinforcements and supplies. At that point, its a game of attrition and since we've already established the British have a strong military force organized and supplies stockpiled (in such a way that they can pull off the very complex maneuver of a trans-Atlantic flight, so not exactly in so disorganized a state as to be incapable of a more conventional, defensive military campaign on their own, familiar terrain with a supportive populace) they'd have little trouble winning.
B) If, on the other hand, those forces don't exist in this scenario (Say the British Med. fleet gets a sufficently bloody nose, or the land military forces raised are too small), then the government-in-exile can't pull off the feats the timeline says they do even if you can somehow smuggle the Royal Family, a few parliamentarians, and a handful of Redcoats to Canada. Maybe they could hold out for a few years, but in this case they're in the position the stranded French are in Scenario A: trapped in a hostile land with hostile locals, with no likelihood of reinforcement and highly limited local sources of supplies, up against an opponent with an effectively unlimited ability to rejuvenate itself and a strong motivation to continue the war and in the diplomatically favorable position to the other relevant powers (The Americans, being aligned with the Franco-Spainish).
Its the co-existance of two mutually exclusive British positions, rather than the viability of either of the two on their own merit, that's the problem with the timeline.