In stage 3 of the zombie master's turn, you roll 2D6 and compare the result with the existing zombies on the field. If the 2D6 roll is greater, the difference is set aside as zombies and placed in a zombie pool.
That's not right. The 2d6 roll is just a yes/no question of whether additional zombies will be spawned at the end of the turn. It has nothing to do with the number of zombies that you will get.
Upon stage 6, the zombie master rolls 1D6 and takes the minimum value between the roll and the zombies in the pool and then places the zombies evenly between the zombie spawns.
Intuitively, stage 6 seems excessive to me. Is it just another loop for the ZM to jump through to lower the amount of zombies to be spawned?
This is where you determine the number of zombies to spawn. Obviously you can't spawn more than you have in the pool. You only get to spawn if your 2d6 roll in step 3 was higher than the number of active zombies you had at that time.