I'm wondering if they are indeed ravenous, or if this is just their behaviour.
Are they starving? Were they like this before you started this diet?
The reason I ask is that my kitten does this more out of habit, rather than anything. She could be free fed and will still snatch food. She grabbed some pineapple out of my FH's hand the other day - and didn't even eat it - it's the snatching more than the starving - so changing the diet might not make a difference.