I thought a good twist for Zod would be as follows:
Because of the BRAIN Interactive Construct built by Kryptonian scientists, war, famine and disease on the planet have been eradicated leaving a Utopian society. The Construct had also taken over planetary defense and Kryptonian scientists along with the governing council decided to share this technology with neighboring systems to help protect against common enemies. One common enemy mainly, the planet Apokolips and it's brutal ruler Darksied, were rendered harmless to any planet wielding the kryptonian tech.
The tech also rendered great Kryptonian warriors who had protected the planet in decades past useless. Warriors like General Zod. These warriors were given positions among local and planetary governing bodies as figure heads and in some cases like Zod ambassador titles. This disgusted some like Zod who's lives were dedicated to the Kryptonian military and who craved war.
Zod eventually ended up as the Kryptonian Ambassador to Apokolips. Darkseid had agreed to this after five years of silence and had finally announced a new era on his planet and called for his greatest adversary from Krypton to observe the changes. Bringing Zod closer to him, Darkseid began to work on the General's hatred of the BRAIN Interactive Construct and powers that created and approved it's use over his military.
Darkseid, through an intricate web of seduction, was able to turn the General against his own planet. Armed with an Apokolips engineered virus, Zod traveled back to Krypton and rounded up a few of his most loyal subservients to help undertake the dastardly deed of corrupting the Construct.
When this actually happens Zod is discovered by Jor El and arrested along with his remaining cohorts. The virus was thought to shut down the planetary defenses and allow for an attack by Apokolips but it appeared to be caught in time. Unfortunately this was not the plan and the virus was not caught in time. The Virus, by design, created BRAINiac and BRAINiac eventually destroyed the planet via the thermo-core wells that supplied Kryptons power.
I think this can be as brief as possible in the beginning of a first film and then we wouldn't see Zod and the gang again until a second or third film. We would also not have to see Darksied or Apokolips at all here. It could all be explained in different ways so that the audience understands what transpired.
CW