I believe I understand the rational behind the separate Completion/Start time parameters and increased control, but are there some default values to get the comet to begin and end within the duration of the track on the timeline?
Constantly adjusting stuff to do what on the surface should be nothing more than a simple DVE move seems crazy. Too bad there isn't a path track available like the text tool has.
Start with a new instance of the Comet filter applied at default settings to a solid color layer
Set the Destination Z value to -100
Set the Completion time to 50
Set Source XY just on outside of the visible layer area in the comp
Set the Destination XY to the center of the comp
Now when you preview the result, the comet should fly on screen from the left and the effect should complete just a couple of frames before the end of the layer in the timeline.
Please let me know if this works for you and if not then let me know how I can help you generate the effect by describing exactly how you would like it to look.