I've gone through FR 3 times, each time picking each starter, only ever coming across entei, I forget which one I picked to start with for him.
I've added more relevant info in the original post. You must have chose Bulbasaur to come across Entei. The legendary should have an advantage against your starter.
Choosing Bulbasaur you'd encounter Entei, Charmander for Suicune and Squirtle for Raikou.
I did the exact same thing, the Master Ball just suits Mewtwo so much in my view.
You're very patient if you choose not to weaken it haha!