I'm afraid that I have entirely bad news for you.
First, the boat:
Yes, Luxe barges are beautiful. No, they do not exist in North America. The canal era here was very short-lived, since most of the continent was settled after the invention of the railroad. And no, there are not any similar types of boats.
Second, living aboard:
While it is possible to live aboard in certain places in Canada, primarily on the west coast, in general living aboard is legally and practically problematic.
I spent several years living in Manitoba. I was back there 14 days ago. I stood on the shore of Lake Winnipeg and looked out at an unbroken expanse of ice. Yes, that's right, ice on May 11th. Ice that's 4 feet thick in the winter. When it's -30, without the wind chill. Ice that moves around with the wind, and just a few kilometers from where I was crushed entire houses:
Manitoba homes crushed as 9-metre high wall of ice slams into them | Canada | News | National Post
I assure you, there is no living on boats in the winter in Manitoba. Any by "winter" I mean "October 1st through June 1st".
Fourth, inter-lake navigation:
While the main rivers (Red, Assinoboine) in Manitoba are navigable, almost every single lake is landlocked. There are some large lakes with geat boating (Lake Winnipeg, Lake Of The Woods) but boats have to be trailered between the lakes.
Sorry to be the bearer of bad news,