What can I adjust in Civ to make it so that my cultural boarders never stop expanding? i.e. the entire map is eventually covered in culture...

Can this even be done?

From my experience with getting forts and colonies to expand culture, I would say it is possible but difficult. Some programming in the SDK should do it...but why in the world do you want this? Even if you had it working, the AI Civs would likely expand to the point where you would not be able to even travel between your cities. Certainly it would appear to work if the AI Civs' culture did not expand either but you would lose the ability to impede your opponent's movement when nearing a large city that normally had expanded its borders. One foray by 3 or 4 knights near a large city could quickly bring it to its knees.

I've set up my own little private Mod to only allow one city per civilization... which I like.

In all honesty... I like my method better... the "cities" actually become "nations" in a way.

Either way, how can it be done?

To each his own. :)

Since you have explained your setup, you could possibly achieve something close to what you want by editing the XML files for buildings that add culture. I haven't looked at it but at first blush I think it would be an easy solution.

Negative... for... whatever reason... there seems to be a "maximum" area that cities seem to hit when it comes to Culture.

Yep I realized later after I posted that if you only have one city per civ then that city would be the capital and the palace does produce culture.

Just another suggestion if this is something you really want and don't mind a lot of trial and error, you could try building something that normally gives culture but change it to a negative number.