The Emoriim were lying in ambush in the route that the B’nei Yisroel were to come through. If they were anyhow going around them there was no need for the Ness. When the mountains come together it becomes flat straight ground. Assuming the B’nei Yisroel were already higher than the ground of the foot of those mountains, coming together was leveling out the ground for them.
Your Pshat about Bilaam hating the Jews more than Balak did, is the Rashi mentioned by Simcha. The question was about the rest of the Parsha. We see that after the initial call, Balak also uses the term Kava Li.
I mention the Aron since I remember that the Aron went ahead for that purpose. This was only during the Ananim. Perhaps one caused the other to flatten it. The Aron brought the Hashgacha out onto the open areas and the Ananim did the flattening.
What you say about the story of the Amoriim happening after Aharon sounds very good. The only question is that we learn that the Ananim returned in the Zechus of Moshe Rabbeinu. Obviously, it didn’t return instantly because the Kenaanim found the Jews, and there was probably some time for people to realize that the Ananim was in the merit of Aharon — just like the Be’er returned in the Zechus of Moshe and Aharon, but only after a void was felt.