For the Get-Off-My-Lawn-A-Thon I've noticed that on Zombies you need anyone with a shotgun style damage spread or some form of splash damage and for best results on Plants you want, once gain, someone with splash damage or Rose for the Homing; trying to nail someone with a precision weapon is laughably impossible with the Speed boost craziness in effect.
While I was figuring out the best character choice it was frustrating but once you properly understand what character variants work and which ones don't it definitely becomes more fun and you start to understand why you see so many of a particular class or variant on the battlefield.
Once you adapt to the speed a skilled Scientist or Rose player can be a real monster in this particular game mode and I've had some of my best games yet as both of those character classes; 76 vanquishes with a 17 streak with the Chemist and 50 vanquishes and a 30 streak with Rose.