Let me try to paraphrase, and restate your requirements, then analyze them.

• You have your "normal apache web server" - let us refer to this as the "web server"
• Then you have the "sharing-server", which, by coincidence/design may reside on the same hardware. Let us call this the "reverse web proxy", since that seems to be it's function. (Web requests hit there first).
• In addition, you have a bunch of "volunteer" "node-sharing-clients". To me, this should be considered equivalent to a "web farm".

If we agree on the terminology, this is a fairly standard setup, except for the fact that the web farm comprises of voluntary machines that may appear and disappear. The purpose of the "web server" is to provide the "master" set of files.

The only additional suggestion I have is that you consider BitTorrent as a mechanism for re-distributing the web server content to the web farm.