How to setup a LAN network with only one bitcoind client downloading the blockchain?
You need to use connect in your configuration file, rpc_connect is something different, it means that your client delegates its commands to another bitcoind.

If one client connects normally and other clients connect to it using connect = ip.of.main.client it will work the way you want it to.

Conversely you can prevent a node from connecting to anything by using connect = 0.0.0.0.

EDIT : I understand better now. You need to use rpc_connect = ip.of.master.bitcoind on the 'slave' node, and connect = 0.0.0.0 to prevent it from loading the blockchain and you should be all set.