Best online "banks" are not banks at all, but credit unions. some have very lose rules on what it is to be a member. Check for credit unions in NJ. Some only require that you have a certain cell phone carrier, etc..
I like credit unions, because they dont seem to pull as much funny stuff as the banks do. Definitely they are more fee friendly.
And even better, open up a business account.
Research states that have privacy laws regarding what is required. That is the next step I am going do. For some reason New Mexico comes to mind, something I read long time ago, but I don t know for sure by experience, and things change all the time. But check it out.