Very cool, GGFreak. I liked your choices. :)
I would change a few things to fit better:
Unliving: When this model is out of action, you can spend 1 Karma to place a Resurrection die where the model was. The die starts with the face equal to the model's Activation stat. Place the unliving model outside the battlefield as close to the die as possible. At the end of each turn, the Resurrection die decreases by -1 and you can spend any amount of Karma to reduce it by the same amount. When the Resurrection die reaches zero, remove it from the battlefield and place the unliving model back in its place.
Design Choices: Using the Karma cost to place the die makes this more of a player choice than an element of luck. Associated with the Activation stat means that weaker models tend to be quicker and cheaper to return to the game. Bosses and Underbosses are expensive to return before the end of the game. Positioning the model outside the battlefield but as close as possible to the die helps to differentiate if more than one unliving model uses this edge at the same time.
Necromancy: As an action, this model can choose one Resurrection die within 3" and reduce it by -1. Additionally, when a Resurrection die is placed in this model's line of sight, reduce the size of the die by - 1. This model cannot have Unliving.
Design Choices: This makes the necromancer less passive. The necromancer must be near the die and spend an action to reduce it. In some ways, this is similar to the Healer of Mages. I kept your limitation of not being unliving (it's a good idea!).
I have to test these edges, but I believe they are good additions to the Risen society I am creating. Probably Unliving would be the special edge of this society. :)