Can anyone tell me if there's a quick script/piece of software that will allow me to package up my current UI to upload somewhere?

If not, can anyone tell me what files will be required in order to make the UI look exactly the same when it's distributed?

You will need to create a new project and archive your UI addons into a single file along with the appropriate saved variables in the World of Warcraft\WTF folder to save the configuration/look and feel of your user interface addons to distribute to other users.  Instructions should be included in the compilation.

Following emphasis is intentional...

Most importantly, I would verify that you have permission from the authors of the addons you want to include in your compilation.

Of course, but for right now, I will just be exporting the UI to another computer to test distribution. Also, if authors didn't want their addons distributed, wouldn't they not upload them to sites just as these? Just thinking out loud.

What files exactly do I need besides the SavedVariables folder?

Ba-bump-ba-bump-bump.