My production model is basically farmfarmfarfarmfarm and when there is a problem, I send out some herbalists or slaughter an animal or two.
How many total farm tiles do you have and how skilled are your planters? Its actually best to turn off "all dwarves harvest" until you have 2-3 legendary planters. Harvesting gains skill points but isn't affected by skill levels- only planting is. So you need to hoard that harvesting skill experience on your planters (who will actually put it to use). Thus you can go from harvesting 1-3 to 5-7 per plot as quick as possible. If you don't need to save wood for charcoal, consider making potash as a fertilizer. If you use fertilizer you might need to reshape your fields. Fertilizer uses a similar formula to bridges and paved roads. You want multiples of 4n-1 (3, 7, 11, 15 etc) for maximum efficiency. I also disable barrels in my seed stockpile (so someone picking up a plump helmet seed doesn't also cancel planting of sweet pods). If you only get an average of 3 per farm tile, then you are going to need over 100 tiles of farms to provide food+drink for all your dwarves. I typically farm for booze only, and supply my food through butchering and fishing. If I use plant food, its derived products (flour, sugar, syrup) so I don't have to worry about cooking up my last seeds. A line of cage traps throughout the caverns can return massive amounts of food in prepared organs, fat, and meat. You can even use your military to go slaughter hordes of crundels and other edible beasties (sadly no Troll burgers). Otherwise, it takes a very long time to get a proper livestock farm going. Not only do you have to coral 20 of them, but you need to wait a year for hte critter to be fully grown (and ready to butcher). Sometimes I embark with a handful of sheep. By the time I need massive amounts of food they -maybe- have bred enough. In the meantime, they can be milked and sheared for cheese/cloth.
Consider egg-layers as well. While Cave Crocs take 2 years to reach full size, they lay about 40 eggs (20-60) on average per clutch. Pastures some into a room and drop in some nest boxes. You can lock the door/forbid eggs that you want to hatch while your dwarves eat the rest. They are worth x4 as much as standard critters, so while you don't get leather from them their bones are -excellent- trade goods. You get about 80 meat when you butcher a full sized one too. I think Turkeys are the best domestic bird to get eggs from, although peafowls mature in half the time (better for butchering, worse for egg laying).