We made it to Mirial, and made contact with the local Jedi Knight, Xelt Pak, at the Republic Base there.
After a bunch of meetings, we got to speak with Master Yerba, and much haggling and careful trading ensued. Remind me to never haggle with Niwadi...
End results: We're hanging out on the Base for a couple days while they outfit the Starcrawler with a high-end Comms package, which will also allow us to call Master Alize from our travels. This is in payment for the Rakatan data we brought with us. They will also help us translate the Star Map data, but want us to search the ruins of a ship that belonged to a Darth Glovoc, who was one of Revan's subordinates, and had mapped a lot of Rakatan space in this quadrant. This will greatly improve the accuracy of translating the Star Charts, and improve the Jedi's knowledge of Rakatan History.
This mission, should Master Alize agree to let us undertake it, will be funded by the Jedi Archaeology Core.
Other than that, it's just a lot of waiting, training, and more waiting, while the ship upgrades progress.