Don't use combat mechanics
AngryDM writes a piece hereAngryGM writes a piece here about D&D combat (which can be applied to any system, really; they all have such heavy combat focus 'by the book'). His posts on encounters and combat are solid reads, and the 'Zombie Horde' is actually a specific encounter that he uses as an example in the linked post.
His suggestion: don't use combat rules. Essentially, don't shoe horn an exciting encounter like this into the limited framework of battle mechanics.
You can still run a sort of 'initiative' order - take actions from each PC and then explain the results, then narrate how the horde behaves and reacts. This then gives you a 'time unit' to pace things like damage, risk of being turned, position of the 'swarm', etc.
This should also encourage your players to think outside the combat 'box', choosing actions to help disperse the horde that might not have occurred otherwise.