Csrlos,
The criteria for being an NGB in the United States is entailed in the Ted Stevens Sports Act, which is a Congressional Act.
The United States has only one NGB. That would be USA Judo. The USJA and USJF are independent judo organizations, that happen to be group A members of USA Judo, because they meet the qualifications under the Ted Stevens Sports Act. The USJF and USJA do not receive any funding from the USOC. They alone are responsible for the funding of their organizations.
If the USJA or USJF sought to replace USA Judo, the mechanism for that process is found in the Sports Act. The United States Olympic Committee is the ultimate arbiter of that process.
The first place I would start to look, is the laws on the books of your country. Secondly, I would look at the IOC and the IJF criteria for being an NGB, and make sure that the group qualifies. The Sports Act in the USA, has as one of the criteria that the NGB must be able to represent the United Stated in the Olympic bodies.
If there is an election of officers, it just might be easier to vote in your people than start your own organization. If you can't win that vote, well, maybe everyone doesn't see it the way you do.
If that fails,
Assuming you live in a free country, nothing is stopping you from starting your own organization. You worry about funding. Well, build an organization that is worth money to your constituents. If you can give them better value for their money, you'll succeed.
Rank recognition might be a problem. That can be solved if you have someone with a connection to the Kodokan, and you can get a process where your students can obtain Kodokan rank. You can also simply disregard recognition of rank internationally, if most of your members don't travel. Those few members that want to qualify for Olympics, can simply join the current NGB.
Be careful what you wish for, because you just might get it. Truthfully, there is judo politics at all levels, and you will be trading one set of politics for another.