Professors, for better or for worse, are notoriously bad at responding to emails in a timely fashion (or…at all). It’s not uncommon for university professors to let emails go unanswered for weeks or even months sometimes. It’s true that there’s not much else you can do besides try them again, but one thing you could do is arrange a visit with the departmental secretary and see if you can catch any of them in their offices, if their office hours are listed. (Graduate students, on the other hand, are far easier to get a hold of, and the departmental secretary may share some contact information of grad students who are willing to be contacted by prospective students.)
I’m not in your field but your profile looks relatively strong to me. The keys are going to be the quality of your research experience and those recommendations.
Also, bonus points for the Arrested Development reference.