If there is no way to do it in DirectAdmin directly, you could use a service such as mover.io (https://mover.io/connectors/, supports WebDav) as a MITM. Sadly this does expose all your user data to a 3rd party.
Alternatively you could set up a cron job to run a few hours after any backup (or a day after if you don't have a daily backup) with a script/command to take all backup files and push them to WebDav.