Maybe leave the French in charge longer? Or make them better rulers, so that Canadians really feel French; then when they rebel against the British, the 13 Colonies feel like it's their 'duty' to help the motherland.
IIRC the colonists didn't hate Britain until there was a lack of threats towards them besides Britain. (The French, the Indians, etc).
Then have the UK adopt a more 'overseas England' policy, instead of a colonies policy, more like what they did with Newfoundland.
Finally, when BNA goes independent, it is a commonwealth realm, while Canada (a free realm with a Bourbon king?) celebrates their day of freedom.