This is a question that I definitely need to answer if I wish to be recognized as original. There's a lot of research to do before I can say for sure, but I think I've found at least one thing that's novel. Omnilibertarianism endorses a new kind of freedom: the freedom of identity.
The beauty of the freedom of identity is that it fuses the notion of freedom as choice and freedom as self-determination into an elegant whole. As much as is possible, everything should be free to become what it wants to be. This is a transhuman freedom, in the sense that it ought to be extended beyond humanity, to apply to as much of the world as possible (ideally, I mean).
Of course, there must be limits to the kinds of identity choices we can make. These come in a variety of forms. First, there are limits to what is physically possible. As we observe, experiment, and learn more about the universe, we may find that the limits are different than we thought they were. Nevertheless, some things are just not physically possible.
Second, there are the limits of what is technologically possible. Perhaps there's a way to travel faster than the speed of light, but it may be that we will never have the capacity to do so. In a narrower sense, we can talk about what is technologically possible today (as opposed to what is technologically possible at any future point). Determining what will be possible tomorrow will require the third kind of limit.
That is, legal limits. Laws should be in place that discourage individuals and organizations from choosing things which threaten the freedom or well-being of others (whether individuals, groups, or civilization as a whole). This means something like the criminal justice system that we have today, but possibly with new forms of punishment. This would also mean regulations on the development of technologies to ensure their safety and effectiveness, laws to protect the environment, and a whole slew of other legal measures which must be put in place to ensure the perpetuation (and hopefully the further growth) of civilization. (This third category entails quite a bit, so I may have to break it up further later.)
The limits that we set (the legal ones, which can also have an influence on the technological ones) must be enabling to freedom of choice. To do this, a government must also be enable to ensure its own survival. Part of this means adapting as conditions in the world change. But, government (regardless of its form) is something that we create, and so it is up to us to ensure that the laws keep progressing along with everything else. The US Constitution gives us a fine example of a small set of governing principles which must be held constant as other laws change, but which are even themselves susceptible to revision with sufficient democratic support.
The freedom of identity, the right of every individual to bodily and mental self-determination, must become one of our core governing principles. Not only should individuals be able to pursue happiness according to how they understand it, they should be free to become whatever they wish, within the limits discussed above. In short, Omnilibertarianism advocates the creation of new rights for individuals. (As for groups and the question of whether and what rights they have, that is something I need to think more about it...)