I will put my plug in for BSPhi. Each chapter is very much like their own. We all share the same principals, meanings, rituals, etc. but there is a lot of flexibility. There are also different types of chapters. We have online, career, and traditional chapters. And each has different monthly meeting requirements.
I know the feeling of wanting to start your own GLO and it may seem some what difficult when you aren't a part of a GLO in college, but community based organizations can be wonderful and can fulfill the sisterhood bond you are seeking.
If you have really thought out all aspects of starting an organization I wish you the best of luck.
But you should also look into other organizations and give them a chance. Beta Sigma Phi is known as the Friendship Club by some. We welcome women of different backgrounds, ages, locations, etc. Every state in America and Province of Canada has at least one chapter so there are so many opportunities to meet women all around the world.
If I were you, I would at least email National and ask. It is sooo easy to start your own land chapter as well. All you need is seven women.
And National will gladly guide you to starting your own.
If you have researched and found that for some reason these organizations can't offer what you need there might be other ones such as the Lion's Club. But if you want to start your own organization just know that the road is a tough one. But if it weren't for people like that none of our GLO's would have been established...and when I think of it that way, you have my support. Best of luck.