I fixed it! Now everything runs perfectly. Here's what I did, step by step (for any future reference).
1. Opened up Grunt.mdx in Warcraft 3 Viewer
2. Exported Grunt.mdx to "My Mods\Mountain Orc" (it is important that the folder that contains the mdx file and the textures (.bld) is in the Warcraft III folder in Program files)
3. Exported the Grunts .bld textures to "My Mods\Mountain Orc"
4. Converted .blp to .tga, edited the skin and saved it. Then converted it back to .blp in the Warcraft 3 Viewer.
5. Opened the Grunt.mdx in "...\Mountain Orc" with MDX Pather and changed the route path for the original skin to the route path for my new skin. (It is also very important that the skin and the model file are in the same folder if you use the MDX Pather)
6. Imported the new model file into World Edit (no need to change the route path). In the editor you can see your new skin, but in order for the unit to appear in the game you must import the skin as well... which is step 7
7. Imported the skin and changed the route path to that of it's origin (That way the model file reads the same route path as the game).
8. Save the map, restart the World Editor, test the map. It all worked perfectly.
(Ps. I hate going to threads where the person says "I fixed it!" and you're like "I have the same problem" and then they don't elaborate on what they did. Plus the method I used is somewhat different than the tutorials, seeing as they never specified where to put the folders. It only seemed reasonable that they should remain in the "Program Files\Warcraft III" folder because I try to save a map with an imported model/skin that is from outside the Warcraft III folder (and I have specified the route path) I get an error message. From what I learned today, the game automatically puts "Program Files\Warcraft III" on the route path of a file if it is a custom route path).
My troubles may have been due to that fact that I'm working on Windows 7.