I think you need to get with a local guy. While working in Afghanistan as Electrical technical Inspector I had the opportunity to work with guys from every state in our country. The only thing that I can say is there are different codes that apply from area to area. The NEC is the national code which is the minimum standard, there is still the state, county and city codes that are out there. In Oregon the violation is exposed cable. The boxes are are legal but you could have a regional code that requires whether proof boxes in a basement? Get with a local guy or ask the inspector for some help. If you just want to clean it up put all your wiring in EMT, flex conduit or MC.
Steve