I think Perspectives would serve you good, as it looks like you have way more tasks scheduled for today than you will have a chance to execute. Then you could save the Forecast for tasks that are truly due – that have to be done today to avoid consequences.
As the Forecast view currently only can be sorted by date (and time), the only way to reorder tasks there is, as you have tried, to change the due date or due time. The exception is the optional part of the Forecast view with a Forecast tag. There the tasks may be reordered manually, by dragging or by using the keyboard commands.