Sibling comment mentioned rclone, which is enabling piece of software and much better at webdaw than davfs2
As it happens, I've been deep in the with rclone, webdav, and Nextcloud over the last few days.
It works. It's slow when synching a ton of small files but besides that I haven't run into any unexpected problems.
If I did it again I'd probably use the Nextcloud client in API mode. But this was originally supposed to be a small project... Oh well.
Rclone works but is still not very good, either it doesn't allow a lot of the things you'd expect from a filesystem or it'll just consume tremendous amount of disk space while it slowly transfers the files to the remote host (even on a really fast link).