I'm not usually big on crowdfunding, but this is the sort of thing that it was created for. I would think that if you made your pitch compelling you'd be able to raise a fair amount that way.

I would also suggest that you really pear down your app so as minimize expenses. Use only one developer, making something with just enough features to get people interested and signing up. I wouldn't spend too much on the logo; a good logo is nice, but the question is, how much will it really help you in attracting early adopters?