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Oh no, that way is basically correct. Generally, path operations work on areas enclosed by a path, and for the most part, they won't work using a single open path as part of the operation.
I actually had already typed a reply, while you were apparently editing your message. So when I tried to post, I couldn't, because (of forum security measures) your message had to go back through moderation again. Happens to me at least once a week
But indeed, difference is one of the ways I was going to suggest. Note that in the red blob that you differenced, the bottom part of it doesn't matter. It's only the wave line that matters. So it could have been just a smooth line around the bottom. The most important part is that the line fully encloses the bottom part of the canoe.
You could have gone a different route as well. Instead of extending the wave path around the bottom part of the canoe, you could have extended it around the top part of the canoe, and used Intersection instead.
Another thing that might have been part of problem, was the wave path being made of individual segments. So I was also going to suggest joining those segments first, and then extending that line either around the above water part of the canoe, or the below water part.
But in the end, you solved your own problem
