This jumps out at me. If there's no one at your school who's really working on the problem you want to work on, the big question is really whether anyone will be willing to supervise you on such a project in the first place. The question of funding is rather secondary to this. If a student were to come to me wanting to do a project in an area that I didn't have that much experience with or interest in, I'd be very reluctant to take that student on. Taking on a PhD student is a major commitment. I would first find out whether you have anyone interested in supervising the project itself. If no one is, you either should look at transferring to a place where there is someone with expertise in that area or taking on a different project.