The question about whether a given six-body celestial system in a given configuration is stable is a research-grade question in the subfield of mathematics called dynamical systems. If I were able to exactly answer your question with support from mathematical proofs, I could probably publish a couple of scientific papers based on my work. Perhaps even a book. But I can tell you what the answer would probably be: No.
The reason for this is that gravitational dynamics are a chaotic system. This means that tiny changes in the initial conditions of the system lead to major changes in the outcome. Any system with more than two bodies is chaotic. Even our own solar system is chaotic; see this page. In the span of a human lifetime, or even the span of all of humanity, it looks like our solar system is unchanging. The planets maintain their respective orbits, and it seems they will forever. But in reality, this time span is tiny compared to the age of the solar system, and even tinier compared to one trillion years. Even with the most precise measurements and careful calculations, we cannot predict what the solar system will look like even one billion years in the future, .1% of your time span. It is almost impossible to find a stable three body orbit, and even harder with six bodies. Even if your system is stable, the tiniest change (like star passing within a few lightyears of the system) would throw off the stability on the time scale of a trillion years.
Since you have altered the time scale of the problem, I will augment my answer, which is still no. Our own solar system is not stable, and so I doubt that your somewhat more complicated system would be stable. That being said, an orbital system being stable is a very stringent and rigorously defined condition, and is not what most people mean when they say stable. If you mean "the description of the orbits I gave remains valid for several billion years," this is a much less stringent condition which changes the answer to "probably not." Several billion years is still a long time. The Lyapunov time is the the time scale on which a system behaves in a predictable way. The Lyapunov time for our solar system is about 50 million years. This means that we have absolutely no idea what our solar system will look like in 50 million years. And there is no reason to expect that it will look anything like it does now. Your system likely has a similar Lyapunov time, so while it may be have nicely for a few million years, it will probably devolve into chaos long before you hit the billion year mark.