In the API response we don't make tasks "jump" to the top - the position is kept in priority order, and should still be located under the section it belongs to.
Of course, this isn't a terribly elegant way to do it. We're currently considering how to handle Sections in the API in a better way, but we don't have a concrete plan for it yet and it's not yet on the actual roadmap.
But in the meantime, you should be able to get the project, as you said, and just look at which Section (i.e. a task that ends in ":") the tasks come after, and you're set!