I have two routers loaded with DD-WRT v24SP1 which can only maintain a persistent link after power cycling when encryption is disabled or set to WEP. (WPA <I>will</I> work immediately after being ...

Run WDS to just extend the existing AP via the wired ethernet connection to the new AP. This should work just fine for what you are doing. I'd still install DD-WRT just for kicks as it's allways been ...