My interests were more intensely in philosophy and theology entering college...A dual degree is obviously quite an investment of money and time - is the J.D. component really providing any tangible and worthwhile opportunities?
Considering the original intent of your question and the thought and research you've already put into this query, it seems the M.Div. is the degree you are definitely planning to pursue and the J.D. is the option you are considering, not vice versa. Speaking as someone who is making this decision myself, I have determined a few key reasons the J.D. is compelling:
1. You are marketable. In a difficult job market, any advantage you have helps your resume work its way to the top of the pile. You can get an M.Div. or M.T.S. or Ph.D. and have obvious advantages over someone with a bachelor's alone, but you'll likely still have to spend several years gaining experience before you are considered for a management-level position. The J.D. will give you the decision-making skills to confidently apply for and work as a decision-maker. Considering the cost of the J.D., take into account that many non-profits offer debt-repayment plans depending on the amount of time you work for them and the type of work you do.
2. You are credible. No matter what the perception of lawyers, the perception of people who have successfully completed a law degree is that they are hard working, logical problem-solvers. Whether you're hoping to work in a church or a charitable organization or an international relief group, the credibility you gain with a J.D. will help you beyond the intellectual gains you've made through law school. Especially if you are working with people of multiple backgrounds/faiths, having a J.D. gives you clout you might otherwise lack with the divinity school alone.
3. You have options. The J.D. gives you the option to work in an area which has nothing to do with religion, but without it your options are limited. That said, disregard warnings against the J.D./M.Div. only being useful to people who want to find a special niche. What's wrong with a niche? My management experience has taught me having a niche is a good thing. Some of the best management books on the market today, including the StrengthsFinder series, laud the development of your niche. You're not cornering yourself, you're specializing, and that seems to be what interests you.
These opinions were formed through research (likely very similar to your own) and conversations with friends. One friend is in her second year of divinity school at Yale, and she's considering a J.D. or an M.B.A. to help her get the kind of job she wants and to avoid possible negative stereotypes as someone who is purely academic or, worse, who can preach but cannot "do." Another friend completed his J.D./M.Div. at Emory (his first choice was Duke, if it matters, but he ended up loving Emory) and now works as a manager at my home church in San Antonio, which has membership over 10,000 and supports a multitude of charitable works. A mentor of mine from years ago received his degree (not sure which specifically) from Princeton divinity school in the 90s and worked at L'Abri (a theology/philosophy community of learners in Switzerland) before becoming an author and college professor. He did not pursue a law degree because law is not one of his professional interests. In high school I worked with a man in San Antonio who has a J.D. from Harvard and chairs various charitable organizations in San Antonio. Some of his work is religiously affiliated, but most is not. He recently advised me to go for the dual degree if it was a strong interest because of the preparation it will give me in "learning to think like a lawyer and a saint."
I know these comments come late in the thread, but I hope anyone reading this and embarking on a similar search finds them useful.