Turns out that it IS possible to manually add a run to Nike+ (including a detailed route map).
I'm not sure if this is the best method, but here's detailed instructions;
http://mattstuehler.com/post/25593216312/adding-a-run-to-nike-manually
Long story short - I used the RunKeeper site to manually create a run (RK allows you to use Google Maps to trace your route).
RK also allows you to export the run to a GPX file.
Then, I UPLOADED that GPX file into the Garmin Connect site.
Finally, I used Angus Smithson's "Garmin to Nike+" uploader tool to upload the run from Garmin to Nike+.
Works great - the start time, distance, total time, route map - are all recorded perfectly. The only thing I lost is the details of my pace during the run, which I can live with.
Hope this works for you!
Edited: 21/06/2012 at 20:58