Hi JDD,
While I'm not familiar with any degrees out there right now specifically for Religion and Modernity, the University of Southern California used to have a three-tiered PhD program (since discontinued) involving, I think, sociology, philosophy, and religion. This tends toward my own interests in religion and postmodernism. I am presently completing an MA in Christian Apologetics (2019) and am considering pursuing an MA or MA/PhD in Philosophy. I see you've applied to various MDiv programs. This will certainly get you pointed in the right direction, just be aware you may lack the philosophical training to apply to a straight out philosophy PhD program afterwards. (You may study modernity as a component of your theology classes, particularly when studying church history, but you most likely will not be studying the structure of classical philosophical thought and how we came to be we are where we are today.)
Question. Where you would like to teach or do research—i.e., a secular or a religious institution—may impact your goals. Have you considered pursuing Philosophy of Religion as your PhD? Keep in mind that some MDivs offer areas concentration, such as in Christian Philosophy or apologetics, and those areas might transfer well into Phil. of Religion.
Check with the schools you are looking into for their recommendations. Don't be afraid to reach out to program directors or professors with similar interests as yours. (I've had positive responses and it has been even recommended to me.) So long as you keep your inquiry concise, a lot of professors will respond to emails. It's good for business, and it's good for the reputation of the school to recruit students interested in what they have to teach.