A careful reading of the following documentation (which is not exactly what you have) gives the details:
Concept is to leave WordPress where it is, but "make it look like" it is in the Root (just the domain name in URL).
Last piece is to set all this up, then rename index.html or whatever your current home page is, to "expose" WordPress's index.php file. But, be aware that a very small number of web hosts actually will display an index.php even when an index.htm(l) is present.
By the way, this is my preferred method of running WordPress (out of a subfolder) as it makes later switches much faster, as you just change folders.