I figured it out.
If you want to do what I mentioned above (have a file with a new file extension run as an executable), from the explorer view:
Choose Tools | Folder Options | File Types (tab) to view the extension associations.
Click the "New" button and choose the Advanced view.
Enter your new file extension and choose Application from the Associated File Type drop-down menu.
It's pretty basic and it seems like I've done it before, but if anyone else has this problem now, here's the solution. :)
Alternatively, you could do the same from the command line by typing:
assoc.foo=exefile
Where "foo" can be whichever file extension you wish to run as an executable.