Religious Apocalypse Zombies. What's the plan?

These would be "Magical" or "Religious" undead. So there's no decay or weathering them down. They are animated by pure force of Godly will. All Zombies killed throughout a single day reanimate the following night. (this creates a persistent threat) However they also follow rules that allow for survival.

Scenario : The Apocalypse begins midday EST. It is Spring, mid April-ish, middle of the week. There is no warning. One moment everything is normal, and the next the dead are rising from the grave and trying to eat people. The water and power will stay on for one month before complete shutdown. The Military and local Law Enforcement is in shambles and it's a total "Lord of the Flies" situation when encountering other groups of people. You may run the scenario as if you have 3-5 other people with you if you want.

1. Walkers and shufflers. No running, no super strength.
2. Headshots are kills, dismembering them slows them down but does not deter them for long.
3. Sound is the most common way for them to detect people. Sight as well but greatly reduced range from normal human sight, and no to the smelling you thing. BUT as they are "Magic" Zombies they have an unnatural "detection" when they are within 5-10 ft of a person.
4. They will lose interest and wander off after several days of no contact. So if you could bar yourself someplace safe you could "wait them out" so to speak. BUT the detection rule is in effect, so if you lock a bathroom door and they are close enough to detect you, they will not leave.

What's the Plan?