I think pretty much what I need is in the title. I'm looking for one person who's managed to do that, and how. I would appreciate it. I tried Cyber Duck, and it let me down
Embrace and extend is Microsoft's method of making sure that only MS products can be used. A SharePoint server may be based on WebDAV, but is not compatible. I would suggest using a standard WebDAV server as the backend.
BTW, I have the opposite problem. I have a Windows phone that will not connect to a WebDAV server. The phone only accepts a SharePoint server.