I did this just today, and it works, so I thought I'd pass along the few little bits of relevant info I learned in the process, just in case anyone else wants to give it a try.
To do this, and have a nice articulated male doll with a fairly normal sized head, as opposed to an articulated doll with a giant head and an ok head on a body with the Least Poseable Ken Legs Ever is fairly easy.
Using the hair dryer method, pop off both heads. Remember the Ken has to have the Fashionista style neck, older Ken heads will not work. If you compare neck pegs and the inner holes in the heads, you'll notice that the LIV peg is a little bigger and the inner hole in the head is about 1 mm wider. I sanded the hole inside the Ken (actually Ryan in my case) with a dremel until it was the right size. If you have a light touch you could probably use a craft knife instead, but be careful as you don't want to split the vinyl.
Using hair dryer again, pop the Ken head on the LIV body.
My results? The head is a near-perfect fit. Posing is a little tight at that joint and I might dremel the inside a little more, or just keep wriggling now and then to stretch the vinyl comfortably.
Sorry for the lack of relevant pictures, but my new camera hasn't arrived in the mail yet.