I do a lot of weight lifting and indoor cycling, and they have helped me get high-quality sleep and have much more consistent days.
I think it would be hard to get both get a lot of exercise and not sleep much. Exercise improves sleep, and when you are sleep deprived, it is hard to get energy to exercise.
Professional football players don't deadlift, for instance. They do a lot power cleans and variations. Deadlifting can be very taxing (although it is one of my favorite exercises).
Evening exercise won't do anything and will probably make it worse, e.g., body thinks it needs to stay awake to party / dance / get some lovin. Evolutionary psych basis possibly?
Military, school, work, life in general. Keep those three going, and you are operating at peak performance.
PE recalibrate a lot of things in me, I sleep earlier, fall asleep faster, goes deeper.