Welcome to the Alliance-in-Exile! Your character sounds awesome.
If you didn't already know, the Galactic Alliance used to be one of the largest lightside majors on Chaos. Since we decided to close up shop and downgrade to minor last year, we've joined up as an affiliated minor faction to the Outer Rim Coalition! There are still GA/AiE characters around, although most of our storyline is progressed these days through either participating in ORC threads or interacting with other factions in diplomacy or skirmish threads.
As far as Jedi specific information, we no longer have a unified order like the NJO when we were still major, but we definitely have room for Jedi! Ex-members of the NJO and new Jedi that join up with us are referred to as "Shattered Jedi", basically think post-order 66 in the movies. We're hunted, on the run, but we're still helping where we can and trying to live by the Jedi Code, Obi-Wan on Tatooine style.
Feel free to join us on discord, you can find an invite stickied in this forum or on the faction home page I think. We also hang out a lot in ORC discord. Looking forward to writing with you as well!
