But instead only one of the many linked clients work correctly (I only start one client at a time, of course), and all others pop up the message:
How did I think wrong?
Bitcoin.org client database files are BDB. They are not multi-user. They can only be accessed by one client at a time.
If you simply want separate wallets, then you can use a symlink to each wallet.dat, and just launch the client each time to access a specific wallet.
If you instead want multiple clients against a single bitcoind, that can be handled through RPC. But that just gives access to one wallet.
If you want simultaneous access to multiple wallets with a single blockchain, the bitcoin.org client doesn't support that. It does appear that both Armory and Multibit do however: