It occurred to me the other day that my schedule is rather like that. All the deadlines for my projects gradually march closer and closer seeming to get faster and faster the nearer they get, until I am overwhelmed with the effort of dealing with them all.
And it also occurred to me that the solution is the same as it is with Space Invaders. You have to shoot down as many of the items as you can while they are still a good way off.
The ideal is to start dealing with any project as soon as you are tasked with it. If you have two weeks to get a report written, use the whole two weeks instead of trying to write it in a panic in the last couple of days. It will also have the advantage that you will produce much higher quality work as well as being less stressed about it.
Instead of dealing with all the urgent things first, try dealing with the least urgent things first. That way they will never become urgent!