Not sure if this can be helpful (and can't validate it works) but it should be easy to add fake elevation tags in the GPX file. One example using Notepad++ (it is free):
Open the GPX file and select
In the dialog box make sure following is checked/selected
Wrap around (in case you don't start at the top)
Search Mode Regular Expression
Paste the following text into the Find what:
and into the Replace with:
Click Replace All - it will take a couple of seconds. This just finds each <trkpt line and replaces it with the same followed by a linefeed, couple of tabs (for readability) and a <ele>0</ele> line. A flat run!
This was almost the exact method I used to upload the track (I matched the <time> tag which always appeared below the trackpoint), and it seemed to work fine.
I noticed the GPX was exported via quickroute but it doesn't seem to have an option for excluding, also a different track with elevation data I passed through quickroute still had elevation data afterwards. I contacted the runner who mailed me the track to get more information on the device/export she used but haven't heard back yet.
According to the GPX standard website the elevation data is optional and should default to 0. For now the search and replace works fine though.
An update on this thread: the watch in question was a Garmin Forerunner 25, however the problem was the conversion method to create the GPX file. Garmin's newer watches save activities as FIT files, which can include a wide range of data including elevation. However when importing into Quickroute, only the track points and times are imported, so the elevation data goes missing. Unfortunately there are not many offline tools for converting FIT files into GPX files with elevation, Garmin Basecamp is the only one I found. Online Garmin Connect is the best option of course, or using the native Garmin integration in MapRunF.
I've used fit-converter.exe at times https://www.pinns.co.uk/osm/fit.html - simple little application that seems to do a good job with fit-GPX conversion. I just installed the Stand-Alone version. It suggests running as administrator but doesn't seem to actually need that, at least for basic conversions.
Thanks for the tip, in fact testing this I realised the FIT file doesn't actually have elevation data in it, rather the data gets added automatically by Garmin Connect and Strava based on survey data. So it seems the only method for such a file is to either convert using Connect or Strava or add the elevation data manually as above.
Edited as I screwed up the first version: I can only guess not having a 25. Within Garmin connect for watches without a barometric sensor for altitude the default is elevation correction enabled. It is under the picture of the watch on the right hand side of the screen. Default for watches with a barometric altimeters is disabled. This is based on the assumption that the barometric altimeter is the best and map/DEM elevation data is better than GPS elevation Try disabling this and re-export the fit file to see if this contains the gps based elevation details.