Well, at least I don't feel dumb for not being able to figure it out!
For some people (like me)—that only need drag and drop task sorting occasionally—this might be a decent workaround. For example, the only time I really need drag and drop is on certain days when I am home and have numerous small tasks for the day (which usually include some errands). To be able to freely move the tasks around as I figure out the precise order that they need to be done in (sometimes because of dependencies, sometimes just for efficiency) is a very big deal. I always have to resort to some other app.
But toodledo subtasks may just do the trick! When drag and drop is on mobile... :)