Abuse hens/roosters.
bringing 8 hens and 1 rooster, letting a few batches hatch and cooking the eggs can yield ridiculous amounts of food with very little effort.
Next suggestion is to dump plenty of cage traps near entrances where creatures appear from in the caverns, if you can catch some giant bats/bugbats/rutherer's and various other stuff, you can seriously get a tonne of food.
If you have access to the surface, just set a hunter, or again, abuse cage traps.
Also, buy food, cook it in lavish meals, resell for massive profit, order more raw ingredients from the dwarven caravan. Still got problems? purchase all animals from the caravans and butcher them all. I rarely use them.
If you're not using masterwork, the amount of eggs you get from chickens/turkeys is ridiculous. I will often remove all food except from maybe 7 plump helmets, get some nest boxes up and cook all the eggs in easy meals. Get 100 or so plump helmet spawn on embark, get the planters busy.
Sound expensive? It is a little, you can probably get away with as few as 10 spawn, not really worth the risk of forgetting to remove them from z menu cook and lose them all and the wait for them to grow can be annoying. It saves on the meat you usually bring, = 60 points taken back, don't even need the plump helmets if you get the nest boxes up fast and cook em fast. so thats 60 more points free'd. so 120 points could be 9 hens 1 rooster and 60 plump helmet spawn and it's way more sustainable than what the default is.
If you have more than 1 planter and get "no plump helmet spawn spam" and don't mind cheating just find the bag with the spawn in, designate a dump on the entire bag, use dfhack to "autodump here" on an area near a relevent stockpile and/or farm plot and voila, you've removed the spawn from the bag.
Vermin could be your problem though. Personally i use cats as ambush finders, i lose a few cats but it's better than losing dwarves, only problem is my entire fort gets covered with rat corpses which need to be moved to the refuse pile and the surface just is a complete mess of random vermin corpses.