my understanding is, you're right, it is not really a yokomen and it is even not really "to-win". I am not affiliated with ASU, but we do the same kumitachi. Saotome says in his DVD the final control is just a defined end of the kumi-tachi as we cannot continue it forever. But it is neither a win by killing, nor the partner's surrender, even if it looks fairly as if.
And the technique starts like a yokomen, but then pushes the other sword aside by twisting the sword and hitting with the side of the foremost third and then moves foreward to lead into the final control, which is clode to a tsuki, but is not aimed to kill, but only to stop the partner.
Unfortunately, I do not have the names, so yokomen-to-win or yokomen-to-finish would be appropriate names to recall the technique, as it seems to be the standard finish in Saotome sensei's kumitachi.
Interesting point on the ending; since we end with one partner opening and "surrendering" I had taken this to mean a "win" for the other partner. It is of course only a kata, so the notion of "winning" doesn't fit well.
I like your description of the final cut; unless I get a real name for that I will call it "yokomen-tsuki", which rolls off the tongue quite well.