To answer a couple of your questions:
As to the calculus, any curriculum worth its salt will require a solid base in calculus. Difficult to understand the theory behind shielding calculations, internal dosimetry, ventilation assessments, activation and buildup, to name just a few, without it. That being said, in practice, most of it gets whittled down to rules of thumb and assumptions or programs that can do it for you.
Lot of statistics in the programs that I have reviewed.
In my experience, I have had minimal exposure (<200 mrem) over the 20+ years I have been an HP.
While there are jobs out there, employers prefer individuals with experience. I would suggest looking at job descriptions for state and federal positions to get a better idea of the current expectations. Will also give you an idea of whether or not there are jobs in that specialty (D&D, waste, medical, instrumentation, dosimetry, operations, etc.)
You are correct in that HPS will probably not grant you access to the online forums without being a member, the HPS website does have public access to the Ask the Expert section which probably answers a lot of your questions. You can also contact your local HPS chapter which you can find through the public access portion.
As to an accredited program, IMHO, you should stick to one that is. My current employer doesn't recognize degrees from programs that aren't. But my employer may be an exception. Doesn't make a lot of sense to spend lots of money on a program that isn't though. My employer also considers an individual's undergraduate GPA even after lots of experience and additional education.