Sageofages,
Perhaps you could suggest to the organization that they set sometime up online to allow donations that they could then redistribute to foster caretakers to help offset costs for the fostering folks?
ETA: Er, they already do
https://www.netpets.org/netp/donation.php. (SofA, did you already mention this? I'm struggling with reading comprehension lately.) But maybe they don't hand the money out to fostering folks directly?
Or if you want to put all your personal info on Greek Chat, which I personally wouldn't, I know that I'd be happy to mail you a Walmart gift card for you to spend on food. (not that the amount I could send would make much of a dent in the overall bill.)
I bet that the number of people who would give money to this cause would be bigger than we could imagine. It combines being about to show support for deployed troops with helping animals; who wouldn't want to help?