I believe you need to import your collection (on your PC) using the network path, not the mapped Z drive path. Go to one of your movies, click the Browse button to change the location of the file, and browse to the network share directly (instead of using Z). At that point it should offer to change all your collection to using that path.
I'm talking about that Path I can see in the first screenshot, Z:\AbouIt.A.Boy... you want that to read \\LIVINGROOM\FlexRAID\About.A.Boy... instead.
Your first goal is to get rid of that Z: path from showing up in the Path Configuration list at all. Only the network share path should be listed there.
I was able to change that movie to a network path by browsing to it through the network share. It did not offer to change all my collection to using that path - any idea how to do that? If I have to maybe I need to delete all my collection and recompile the collection through the network share?