Snares for catching animals...set them at night, check them at night.
That's all I could come up with, as you've covered most of the rest.
If they have cell phones is there some other groups of their own style/beliefs they could bring in? A small army could probably go out at day and forage, collect water, etc.
Thanks! The snares are aometing I have in my own supplies, but I forgot. Good add! Fish traps might be possible. Right now, their biggest single help is that people don't think anyone is there. THAT makes things harder, but I understand. Also, the longer they are empty, the safer they are.
That said, the snares might add to their food supply, with very little risk; since they are quiet and easy to set up!