As you can tell by the comments, your use case is far from conventional or recommended. You are trying to mount and modify an entire filesystem by using an apache process running inside a permissions and security model on that filesystem. This problem will not go away, because Apache is of course designed to prevent remote persons from controlling the whole damn filesystem (including the parts "underneath" Apache or root). So you need to:
- rethink your problem as one that fits inside the Apache model, or
- find some system-level webdav support (unlikely), or
- forget about webdav (most likely).
Probably a combination of 1 and 3. You cannot legitimately want to be able to overwrite, say, libc remotely. This is why we are looking at you strangely. What are you trying to affect? If you are trying to use this to roll out system configuration changes, find an appropriate tool (chef, puppet, etc.). If you are using this as deployment mechanism (say for websites or applications), try a build tool like gradle.
If you are that worried about speed, you shouldn't be remotely mounting a filesystem anyway. For example, when you would prefer to bundle a series of edits and deliver them compressed in a semantic group... then you're talking about git (version control). No persistent connection, nothing more than SSL needed, compressed storage, compressed communication, rollback capability, etc. But even in that case you shouldn't be messing w/ binaries on the running system.