I'd say try to identify possible supervisors and get in contact with them. Even if the uni is reluctant, a supervisor that is truly interested and thinks you have potential can argue your case. The funding bit is a difficult one, but not impossible. This too might be something to discuss with a potential supervisor. So make sure yu get your idaes clear, and have a go! The worst that can happen is they say no, in that case, go for the next potential supervisor...