Garmin Connect doesn't allow you to do this directly. I don't believe any of the other services do either. Not only do you need to generate fake position data, you need to fake time data as well. There will be a lot of fake data in there.
I think the closest you could get would be to create a course, get that data as a tcx, then convert the course tcx to an activity tcx with fake data, then somehow merge that data with the data from your actual activity. It would be a lot of work.
in the future, it might be a good idea to enable Auto Pause, or to consider your water stop as part of your run and leave the timer running.
