You might want to use as a reference book Measures of Religiosity, 1999, by Peter C. Hill and Ralph W. Hood Jr.

A couple articles show up in PsycInfo. Mostly religious addiction is a term used by bloggers rather than by serious scholars of religion, and you should base your study in a serious study of the literature in the psychology of relgion, from a textbook such as The Psychology of Religion, Third Edition: An Empirical Approach, 2003, by Bernard Spilka PhD and Ralph W. Hood Jr. PhD

You should be familiar with various categories used to describe religion, everything from William James' healthy-minded vs sick soul to research on dogmatism. 

Religious addiction: Obsession with spirituality.

doi: http://dx.doi.org/10.1023/A:1014074130084

By Taylor, Cheryl Zerbe

Pastoral Psychology, Vol 50(4), Mar 2002, 291-315.

Discusses the history, recognition as a disease, symptoms and characteristics of religious addiction. This is described as an obsession with spirituality that has not only has harmful effects for the individual but also a devastating effect on the family. The author discusses connections with scrupulosity and obsessive compulsive disorder, the downward spiral of religious addiction, and the effects on the addict, the codependent spouse, and children, including adult children. Recovery, intervention and treatment issues are discussed, including support groups employing a 12-step program. The author includes personal experiences with these issues. (PsycINFO Database Record (c) 2016 APA, all rights reserved)

Religious addiction: The subtle destruction of the soul.

doi: http://dx.doi.org/10.1023/A:1021351428976

By Vanderheyden, Patricia Anne

Pastoral Psychology, Vol 47(4), Mar 1999, 293-302.

This paper acquaints one with and examines critically the reality of religious addiction. It describes some of the defining characteristics and symptoms. Rigidity, black and white thinking, low self-esteem, magical thinking, judgmental attitudes are but a few of the symptoms of this complex phenomenon described by myself as destructive soul work. The religious addict seeks to avoid pain and overcome shame by becoming involved in a belief system which offers security through its rigidity and its absolute values. This paper is not definitive in its scope. It's purpose is to explore and examine with the goal of gaining insight and awareness into the topic of religious addiction. (PsycINFO Database Record (c) 2016 APA, all rights reserved)

Dear Dana,

What an interesting topic. I have done some research on the tendency of people with eating disorders to volunteering time, money, energy and more to satisfy the needs of others while neglecting their own needs on a very basic level (e.g. denying themselves proper nutrition). I am aware that the purpose is different from yours and that the questionnaire I used has no direct connection to religion. However I thought the concepts are similar and you could at least relate to it in your literature review if not actually use the questionnaire. I attach the questionnaire and two articles that have made use of it. Good luck,

Rachel.

at the risk of totally offending sensitivities, if we strip away all the philosophical overlay (like inferential value judgement of what the afflicted person is doing) the question could be re-phrased as "what psychological or psychopathological qualities correlate with a tendency to self destruction whether by slow or rapid means".   and the answer would be "psychosis" (whether specifically matching DSM or not quite.   This label is found to fit people with eating disorders in studies that dare to investigate with serious tools like MMPI.   and there was (maybe 20 years ago???) a paper by a chap (possibly last seen in Belgium, if I remember correctly, trying to contact him) who did MMPI on both Israeli and Arabic terrorists (ones captured live that is, but - again from memory - with the idea of self destruction in mind) and came up once more with a rather coherent set of MMPI data to indicate psychotic tendencies with pseudo religions overlay merely a sort of camouflage for seriously disturbed thinking.   Your question (just like those two categories) could comfortably hide under altruistic carpets, but as I suggested, if we take away all value judgements that we might make of what they do and who they are doing it with and for, we are potentially left with "disturbed/irrational or at least lamadaptive thinking" regardless of whether a few people in long robes thrive off their disturbance.   so I would say, first do an MMPI, and then see what is left to discover.