Well, there is WebDAV. At least Windows and OS X support it (Windows from Explorer, OS X from Finder), no idea about mainstream Linux/Android/iOS support though. Also, no idea if WebDAV can deal with Unix or Windows permissions, but I did not have that problem when I set up a WebDAV server a year ago.
IIRC WebDAV uses GET for retrieval, so the read parts can be cached by an intermediate proxy and the write part be relayed to the server.
As someone who once tried to write a WebDAV server I cannot with good convince recommend it. It's Bizarre extended HTTP protocol that should not exist.
Out of curiosity: why did you try to write your own WebDAV server? Apache ships a pretty much works-OOTB implementation - the only thing I never managed to get working was to assign uploaded files the UID/GID of the user who authenticated via HTTP auth to an LDAP server.
More specifically a CalDAV server which is a bizarre extension of WebDAV that shouldn't exist. We wanted one to connect to our internal identity server. That project was abandoned.
Actually i thought about Gopher (i even have my own client - http://runtimeterror.com/tools/gopher/ - although it only does text) since it basically behaves as FTP++ with abstract names (sadly most modern gopherholes treat it as hypertext lite by abusing the information nodes).
Gopher generally avoids most of FTP's pitfalls and it is dead easy to implement.
