Do you really need funding, or do you need financial motivation to do the work?
I would suggest if you really do need some funding for some specific costs, you should take as little as possible :)
Do you know how the Facebook grant fund works exactly? They reserve the right to be the first to invest?
"I would say multiply the number of team members by the time period you're asking to be funded over, by a very high valuation of your team members' time ($75/hour, say), and add some server costs."
For anyone curious, one of the facebook platform ideas was to make a Sim City type game for the facebook platform where your city got bigger and better as more people viewed it or you invited them to make their own neighboring cities.
Kind of like this French site, where you build a city by having people go to your web site. http://rms.miniville.fr