@adam_t, Thanks for clarifying. When you wrote “Yes, exactly like that” to my My Tasks list view screenshot I didn’t assume you were discussing instead a project view, and board view of that project to boot!
First, since you are describing tasks assigned to you (I believe) I recommend using My Tasks view not a separate project view which will both involve extra effort on your part and somewhat go against Asana’s expected use which often can cause further trouble. You can create five to seven similar sets of those sections I showed in my screenshot to correspond to a workweek or week if that’s what you desire, or have less subdivided section buckets for, say, Tomorrow, Day After Tomorrow, and Later This Week so it’s more of a rolling view for tasks beyond Today.
Second, I feel you’ll be able to see more of what you need to focus on with list view (and can still drag and drop) rather than board view so I’d tend to recommend list view for this. At the moment that’s fortuitous because My Tasks does not support a board view–but it will; see Upcoming changes coming to My Tasks in Asana! [breaking changes] for details, which is written for developers but I think you’ll be able to see how My Tasks will be updated–you’ll get your board view and the ability to toggle between list and board view.
By “see more of what you need to focus on with list view” I find for a need like what you describe, I’ll be focused primarily on tasks found in the current section (“Morning”) or nearby ones. In that case List view gives the best view regardless of how many tasks are found in these focus sections because a task is only one row tall and also takes up the full width; board view turns tasks into cards so you can’t fit many, and instead always presents more columns (sections), but you’re not focused on most of them so it’s not the best utilization of screen real estate for this need.
If you prefer to use board view I would second a couple of @LEGGO’s suggestions.
Larry