The main difference: hot yoga is usually a vinyasa flow that varies each time you attend a class. It's like regular vinyasa with an extra element. Bikram follows the same sequence each time, is slightly hotter, and has more breaks. I'm not a regular Bikram practitioner, but it sounds like practicing often will align with most of your goals, and if you need a little variety, you can always do a hot yoga class.
P.S. The "new age" spiritual stuff, when presented correctly, is actually based on ancient scripture and tradition. I hope people aren't out there teaching naked yoga Scientology!
