Is there a way to Split one 42 Inch TV into Multiple Displays or Virtual Displays?
You wouldn't necessarily get "sharper" resolution - splitting a 1080p HDTV into two monitors side-by-side would result in two 960x1080 displays:

+----------------+    +--------+--------+
|                |    |        |        |
|                | -&gt; |        |        |
|                | -&gt; |        |        |
|                |    |        |        |
+----------------+    +--------+--------+


Is that what you're looking for? Despite the admonishments in your question, I don't think that's really what you're looking for. You'll get the exact same thing by just resizing your FCP windows to take up half the screen and putting both of them on the same screen. (You're stuck with the 1920x1080 pixels your display has any way you slice it.)

In (more-direct) answer to your question: no, I don't think such programs exist.

Note: I'm not familiar with Final Cut Pro, so I'm assuming it's multi-screen behavior is implemented with multiple windows.