.... Is there a simple program that will do this? ...
Probably not, but one you might try is TrackMaker ( http://www.gpstm.com/
). It has the abilty to load an image file and allow you to calibrate it as a map. It also interfaces with most brands of GPS to allow up/download of waypoints, tracks, and routes.
If you are able to find a suitable aerial photograph, use your GPS to find the coordinates of some easily identified points on the photo and then calibrate the photo in TrackMaker. At this point you should be able to load your GPX file to your "map".
I've used TrackMaker to reverse engineer a 200 waypoint route by merely knowing the coordinates of one waypoint when all I had was a photocopy of the layout of the route, without the underlying map.