The native files from the Edge are .fit files, which are binary files not text files.
These can be spliced using the Fit File Repair Tool into a single fit file, containing 2 laps.
If you upload them to eg Garmin Connect as 2 separate rides, then export each as a GPX, you will get 2 GPX format text files which you can then manually splice in the text editor.
So long as the GPX file contains <trkpt> nor <rtept> then you're good to go.
Sounds like what you are already doing is basically correct, but if it's not working, perhaps you're missing a tag someplace ( or perhaps an un-matched parenthesis ?
You can join tracks in basecamp, and that will give you a track.
Not sure how you've got it to be a route.
Why don't you post the strava links to the 2 segments, so I can download them and splice them, and then I'll send you the result, and you can compare it to your own attempt?
Either that, or send me the original fit files and I'll splice those.