Multitask! Fast forward to the Masters (plus Avalon) having met up on the Jedi Star. Then pair up the players and simultaneously run "first contacts" between the Masters and the Padawans. That way everyone is participating in a fairly rapid fire fashion (you wind up in two interactions at once --- one as a padawan and one as a master).
This lets us do initial tests on the padawans, without people having to wait for weeks. If there's no NPC conflict in these vignettes, they can even be self-GM'd to avoid overloading @Rabobankrider