That's not writing yourself in a corner. Writing yourself in corner means you have to pull out a McGuffin or a deus ex machnia to come up with an ending that doesn't fit. (See: Any movie made where destroying the mothership causes all of the secondary ships/attackers to drop dead.)
The writers made a choice to have Superman kill Zod to have a impactful, shocking, moment in the movie. They didn't write themselves in a corner they wrote themselves exactly where they wanted to go. And, for me, it worked. Again, Superman showed pain and remorse over doing it. It didn't come easy to him and that he didn't "simply kill Zod earlier" shows it was his absolute very last choice and not a decision that came to him quickly and easily. (See: Him risking exposing himself to a bus-full of children as opposed to letting them die to protect his identity.)
Where it goes from here, we'll see. But killing is hardly completely out of Superman's character and he'll bring himself to that point if he absolutely has to go there. Again, as we see.
Again, what else were his options with access to the Phantom Zone gone and Zod is just as powerful as he is and is promising to kill humans to his dying breath? Again, this was done much better than Batman shrugging off killing Ras by simply saying "Well, I didn't kill him. I just didn't save him."
I say this as a big Superman fan, I've got no problem with how the Zod thing was handled.