Hey, you made my day. It works pretty well.
As a german user my UI language is german as well and just discovered that your solutions has to be localized for me 
https://nextcloud.[DOMAIN].[TLD]/remote.php/dav/addressbooks/users/[USERNAME]/contacts?export does not work.
But https://nextcloud.[DOMAIN].[TLD]/remote.php/dav/addressbooks/users/[USERNAME]/kontakte?export does.
Anyway thumbs up!
Update: Using curl command in my crontab now. Works pretty well.