Thank you for your advice. Believe it or not, I don't think we would get more than 15 in this group initialy until the other guys see a value in the group.
Many of the women's groups in our church are kinda pushing the active guys to do something to share brotherhood int he church and also promote "guy" type of stuff going on in the patriarchy.
Then why not form a Men's Brotherhood among the 15 of you? You can decide the scope and focus of the group among yourselves. I would suggest at least one social activity a month and one service activity every other month to start with.
For social activities, you could play cards, go bowling, play ball, cook, do woodworking, fix cars, go to sporting events, attend local activities like food festivals or car racing, go fishing, or any other number of activities. See what the hobbies, interests, and skills of the men in your parish are and build around that. You might learn how to make fly fishing hooks or you might put together an accountability program for being good husbands. Whatever you form, you will have little to no overhead and will be able to tailor it to the needs of the men in your parish.
For service opportunities, you could repair the church or rectory, provide security to pro-life sidewalk counselors, do yardwork, give food to a homeless shelter (maybe the food you cooked), or serve food in a soup kitchen, collect religious goods like prayer books or icons for soldiers in Iraq (there is not an Any Soldier program, but you can identify specific soldiers through acquaintances), you could also collect religious goods for Iraqi Christians, collect toys at Christmas or blankets in winter and fans in summer for the elderly, take out homebound parishioners or visit them at home, give homework assistance to high schoolers, teach adults how to read, organize a Mothers' Day Out around the holidays to give moms time to shop and wrap without the kids for several hours, do administrative office work, the possibilities are endless.
If there is enough land somewhere, you could grow your own crops in small plots and sell the fresh produce, donating a percentage to those in need. You could jointly sponsor a Cub Scout or Boy Scout troop. You could work with the Special Olympics. From a study group specific to men's issues (Early Church Fathers, Bible, Saints, practical advice) to sponsoring men's retreats, from focusing on social needs to spiritual needs, you could get a group of 15 guys together, give yourselves a title, and get to work without the overhead costs of a national organization.
You could also do fundraising in many different ways. The money could be put to the charitable and social activities of the group. Some could be saved in order to plan a national affiliation's start-up costs. Fish frys, kielbasa, raffles (depending on state laws), silent auctions, cookbooks, registration fees for non-members attending, dues, placing items in the parish bookshop which will benefit the group, and begging (I mean, sponsorships) could all bring in revenue.
Until you get to that point, why not just start with what you have? 15 guys who want to get together and have fellowship with fellow Byzantine men. A Byzantine Brotherhood would provide what you need and give you plenty of room to grow into something more should you wish.