You're not going to like my response, but I mean it with kindness and hope you can take it that way.
Developing a "good professional reputation" is a legitimate prerequisite for graduate school -- and it is reasonable for a school to want someone in a legitimate position to attest to the quality of your professional skills and behaviors. One of the problems with attending online schools
is that you are less likely to develop the types of relationships with the professors that will come in handy when you need someone to vouch for you. And of course, it's almost always a good thing to develop positive relationships with supervisors and other colleagues who could vouch for you if necessary.
I had a similar issue when I applied for my PhD program -- 10 years after graduating with my MSN. I tracked down my academic advisor (who had moved on to another institution) and got a recommendation. I also got a recommendation from a local nursing instructor who I had worked with in the clinical area and for whom I had done a couple of guest lectures.
Perhaps you should treat this challenge as if it were a prerequisite course you need to take before you can be admitted. Work with a local school, do some volunteer work, etc. that will help you establish a professional relationship with someone who can provide you with a recommendation. It might delay your entry into school, but it might be a necessary step for you.
Another possibility is that perhaps your chosen school would allow you to take a class or two -- with some sort of "conditional acceptance." I served on an admissions committee years ago that had the ability to offer "probationary acceptances" to candidates we felt were worth taking a chance on, but who did not quite meet all of our qualifications on paper.