I think there is a misunderstanding here. As the saying goes: Don't fix what ain't broken. The reason the Jedi operate inside Republic Territory is not because their religion demands it. It is because
that is area of space that welcomes their religion with open arms. Heck, one of the reasons the Republic expands so aggressively is to create more worlds upon which the Jedi can be Jedi and do their Jedi thing. Legally, easily, and with the full support from an entire Galactic Civilization.
Free space will always be free space. But the reason the Jedi have been discouraged from proselytizing or warmongering
inside other Faction's Territory, is not because their religion is against it. Hardly. It's because that is a really good way to get your character killed by another large group of players. Lol.
I think there is a misunderstanding here. The Jedi Covenant was not created because of a simple break in religious precedence. It's because Independent Jedi don't like taking orders. They like giving them.
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So my question would be: Why not just join the Jedi Order and organize their Foreign Policy and Missionary Program abroad?