The hatcheries spawn a different amount of larvae based on your difficulty. 6 on hard and brutal, 9 on casual and normal, rather than 3 larva like in multiplayer. You'll be able to build up more larva with more hatcheries. It is how they managed it in the Starcraft:Brood War days. I'm sure the 300 minerals spent on extra hatcheries is something that is easily affordable in the campaign.
Your other option would be to constantly build units and hope that you have the correct composition. (Which isn't really the zerg way of playing).