I had a look at our production logs. I have several suggestions:
1/ I see "lots" of register-repository calls. You only need to register-repository once; LCCS will store this information for any subsequent recording usage. I would suggest registering somewhere in the admin side of things. Perhaps you are already doing this and were just sending repeat requests because recordings did not work yet. But I thought it worth mentioning.
2/ You are using both the WebDAV authentication and a non-default port. While we support both of these use cases, I would revert to step-by-step approach until you build up to the full authentication and the port desired.
A/ default port and no authentication
B/ specific port and no authentication
C/ specific port and authentication
That said, I was able to both ping your WebDAV server and telnet to it on the default http (80) port.