You misreading the situation on quite few points. First off in the Campaign Wellington fought in Spain the Guerilla's were on his side, not fighting against him. Second Wellington was a great general, not a miracle worker, he has to follow military logic. As he himself said they would need to gain naval control of the Great Lakes in order to invade the United States. The Naval buildup on Lake Ontario was already putting a major strain on Canadian Resources. At the time the war ended the British already had 1 First Rate SOL, and were building 2 more on the Lake, and the Americans were building 2. It's hard to imagine an escalation much beyond that, and if there was it would take lot of time.
Lake Erie is completely under American Control, and they have superiority on Lake Huron. After winning the Battle of Lake Champlain the Americans have full control of those waters. The British would have to build a new fleet of shallow draft Frigates to try again. Of course after the invasion in 1814 Vermont was then in the war, so they can't even get down the Richelieu River to get to Lake Champlain, without invading Vermont first.
By 1814 the Regular American Army isn't tiny, and U.S. regulars at this point were standing toe to toe with British Regulars.
In early 1814 Congress increased the Army to 45 infantry regiments, 4 regiments of riflemen, 3 of artillery, 2 of light dragoons, and 1 of light artillery. The number of general officers was fixed at 6 major generals and 16 brigadier generals in addition to the generals created by brevet. Secretary of War Armstrong promoted Jacob Brown, who had been commissioned a brigadier general in the Regular Army after his heroic defense of Sackett's Harbor, to the rank of major general and placed him in command of the Niagara-Lake Ontario theater. He also promoted the youthful George Izard to major general and gave him command of the Lake Champlain frontier. He appointed six new brigadier generals from the ablest, but not necessarily most senior, colonels in the Regular Army, among them Winfield Scott, who had distinguished himself at the battle of Queenston Heights and who was now placed in command at Buffalo.
Militia was a mixed bag, but some units were very good, and even average units could fight well from fortifications. Invading New York isn't as easy as you think, and invading New England is a bad idea, because it would force them into the war. They were determined to defend themselves, and they had the best trained, and equipped militias in the Union. Massachusetts mustered the following Militia forces during the War of 1812.
During the War of 1812, Massachusetts supplied 43,321 infantry men, 446 cavalry men, 2,714 artillery men, and 200 men in miscellaneous troops for a total of 46,681 men.
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New Hampshire: During the War of 1812, New Hampshire supplied 5,279 infantry men, 642 artillery men, and 34 men in miscellaneous troops for a total of 5,955 men.
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Vermont: During the War of 1812, Vermont furnished 4,853 infantry men, 243 cavalry men, and 140 artillery men for a total of 5,236 men.
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Rhode Island: During the War of 1812, Rhode Island supplied 746 infantry men and 164 artillery men for a total of 910 men.
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Connecticut: In the War of 1812, Connecticut furnished 9,161 infantry men, 137 cavalry men, and 905 artillery men for a total of 10, 203.
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New York: During the War of 1812, New York supplied 63,790 infantry men, 2,415 cavalry men, 8,830 artillery men, and 2,861 men in miscellaneous troops for a total of 77,896 men.
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These are hardly insignificant forces that Wellington with even 20,000 men is going to just run roughshod over. Conquering these Northern States would be out of the Question, New York alone had over 1,000,000 people in 1815. What your talking about is a fantasy, it's just not realistic. The war was going to end in a draw. Going on, just throwing in more men, and ships is a waste of time, lives, and money, for both sides. Nether side was going to win a clear cut victory.