I can see how the Patriots can obtain more of Canada but not all of Canada.
1.) Stronger support in New Brunswick - if there is stronger support in New Brunswick, perhaps the US gets a little more added onto what would be Maine.
2.) Capturing Fort Niagara and Fort Detroit - With the capture of these two forts and being able to defend them, the Americans might be able to recieve what is Ontario today in the Peace of Paris.
For this, you could have no US advance on Quebec, but have the Americans and Arnold advance on Fort Niagara. Keep the Montgomery expedition against Montreal in order to defend New York but have Arnold take Niagara again for the defence of New York. The Americans would eventually retreat from Montreal in a delayed tactic which could still have Arnold defending Lake Champlain in 1776. The Americans keep Niagara as the British want to focus on the Hudson in 1777....lose at Saratoga
The Americans recieved Ohio, Indiana, Illinois, Michigan, Wisconsin and Minnesota by capturing of British outposts by George Rogers Clark. He was able to sucede with scratch forces. Giving him 500 more men to go along with the forces that he had might get him to Fort Detroit.
The Sullivan campaign of 1779 was another chance for the Americans to take Fort Niagara. Have Sullivan be a little more daring, or put someone else in charge who is and have them capture Fort Niagara.
As the British turn South, the Americans keep the northern forts.
When the Peace of Paris rolls around, the British keep Nova Scotia, New Foundland, and Quebec but the Americans keep what will become Ontario, or Upper Canada at the time.
So thus the USA gets the sparsly populated portion of Canada in the 1780's by capturing the two forts of Niagara and Detroit which is not too out of reason for them to capture.