Interesting - I've never had much of a problem with carnivores.
Storms:
Open the shelters as soon as a storm is announced
Send ranger teams into every carnivore paddock - I do this by sending them to resupply feeders, but the goal is to have them nearby when the dinosaurs start attacking fences. When there's a jeep, dinosaurs seem less likely to break the fence.
Recapturing everything doesn't take very long, and so long as the shelters are open, your park rating/money doesn't take much of a dip.
I've beaten Jurassic Sorna, now working on Pena, and this is some of what I've found:
Upgrade your Expedition Centre with max Dig Yield, and always have expeditions running - these end up being your income more than contracts
Save every time you complete a contract, and reload if you receive a new contract that you don't want or will take too long to do
Herbivores: once you have the species number goal reached, check what is the max population each paddock is happy with. Then check what the highest scoring dinosaur in the paddock is, and make more of those until the paddock is full.
Iguanodon, Parasaurolophus, and Pachycephalosaurus score decently well.
Carnivores:
Use the large ones who can share paddocks with their own species, and with a small carnivore species
Baryonyx
Suchomimus
Ceratosaurus
Your park rating will mostly be determined by your dinosaur rating, but once you're not making a loss, you don't have to hurry to get it higher. I tend to sit on expedition income, and raise the fossils I want to 100% before spawning new dinosaurs. Means your park fees don't go up till you're ready. The DLC dinosaurs really help because they give you more dig sites to strip mine.
Stegosauruses are a pain, but they have a high rating, and you can make a lot of them. Combine them with Parasaurolophus and Iguanodon, and you end up with a decently high-scoring paddock.