Carl, actually you can export a .tcx file from Strava. It’s a little known feature. Here’s a tutorial from the Strava site. Give this a try.
"Strava allows you to export .TCX versions of your own activities. This is a little-known trick, however it’s simple to use. Simply add “/export_tcx” - without quotes - to the end of your activity page URL.
For example, if your activity page is www.strava.com/activities/1234567890 - just add the text to give you www.strava.com/activities/1234567890/export_tcx and hit enter. This will download a TCX version of your file to the location specified by your browser’s preferences."