Thanks for the responses, I have now resolved the problem. As was suggested by TM, I adjusted the file path, as all of my permissions were correct.
While I had figured out what the problem was, not being able to read "PHP" prevented me from seeing the solution staring me right in the face.
The issue was that I did not understand that the syntax dirname(__FILE__). represented the relative path for the running script. As TM mentioned,
The function dirname(__FILE__) returns the path to the running script.
This was why my entries were all being evaluated relative to the includes directory, even when I thought I was entering an absolute path.
I have now set it to be
ini_set('session.save_path', dirname(__FILE__).'/../tmp/');
which will give me the expected WEBROOT/tmp location, and is also "portable" if I were to move my installation to another folder/directory.
Thanks again to all who responded with suggestions.
Hope the explanation helps anyone else who may stumble on this issue as I did. Now, on to evaluate FA on its merits.