If you plan a trip that exceeds your template's Route Option for the "End driving at" setting all that will happen is that you produce a route that includes in the Driving Directions a line that says "End of Day" and then it resumes with a new day ("Day Two"). It will resume the Driving Directions with the the time that you set for "Start driving at" in the Route Options.
Now, clearly, you are not going to pull off the highway and just stop there overnight. So all you have to do is to go into your Route Options for this trip only and reset the "End driving at" option to some time later than when the route plan gets you to the destination you desire. This will apply only to the open map and route and will not affect your template so long as you do not save it as a template.
Any changes that you make to Route Options will apply only to that particular route. The next time you want create a new route, just go back to the previous template which will give you exactly the same starting settings as before.