Have you looked at the AACN white paper on CNL role and the differences between CNL and CNS?
American Association of Colleges of Nursing | CNL White Paper
The CNL is essentially an advanced generalist nurse. It is not a supervisory role per se, but the CNL is intended to be a resource for and role model for other nurses. I think the concept is great. It is not an advanced practice role. Ultimately I chose a different program because I would like to get prescriptive authority, which is not an aspect of the CNL.
Also look at the job market. The VA is committed to hiring CNLs but other places are not so quick to get on board. This may change.
As far as the non-nursing programs
, you've listed a lot of different stuff. Sounds like you have broad interests. Unfortunately grad school is not like undergrad...where you can take electives and try different classes. If you like counseling, you could try psych nursing, MSW, or become an LPC after getting an MSN ...otherwise public health is general, as is the CNL, as I mentioned above.