People have specific feelings about Liberty University. It’s not just because of the conservative values (although that, of course, has a lot to do with it). Liberty’s has adopted some practices that make people question its quality. For example, typically college presidents are career faculty with a history of research and scholarship, as well as experience both in teaching at and being in the administration of similar/peer institutions; typically, they are selected because of their prominence in the field after a search of many months. Jerry Falwell, Jr., has his position because he is the son of the original founder of the university. This kind of succession doesn’t tend to inspire confidence in people.
Some of the people who say they might not interview someone with an LU degree may say that because they doubt the quality of the education that someone could receive at a school where common standards of academia are not held. LU has also been open about some of their stances towards certain issues that may make employers worried that students share those stances (I’m not talking about religion or conservative values; I’m talking about things like Liberty’s official anti-LGBT policy, which may make employers with non-discrimination and EEO policies wary).
I think the type of religious employment you’re looking for would matter. Hospital chaplains, for example, are required to be respectful of all faiths and serve people with many kinds of religious and faith traditions and backgrounds. Rightly or wrongly, a person who hires hospital chaplains could potentially see LU on your resume and make some assumptions about your stance/attitude towards people from different faith traditions than yours.
In addition to that…based on your own admission, it seems that some aspects of your previous degree (it being nationally accredited instead of regionally, for example) are holding you back. Why would you add another degree that has some skepticism/dubiousness attached to it? I think expecting to pay only $15,000 for a professional doctoral degree is a bit unrealistic; with super low cost expectations, you may find that the quality/reputation of the programs at that level will also be questionable.
Duke’s Divinity School has a low-residency/hybrid D.Min that only requires you to come to campus five times during the two years: https://divinity.duke.edu/academics/dmin
Emory’s Candler School of Theology also has a low-residency D.Min program that only requires four campus stays: http://candler.emory.edu/academics/degrees/dmin/index.html
Biola, Abilene Christian, and Southern Methodist have similar setups. There are also several seminaries that offer a D.Min this way.
I would also verify your assertion that a D.Min would increase your income. Particularly if you have no experience as a hospital chaplain, and/or if your degree is from a not-so-reputable school, you may find that your earning potential actually doesn’t increase that much. My understanding is that an M.Div is actually a terminal degree in terms of practicing as a chaplain.