Looks like you're off to a good start.
I have a Twilight Imperium RPG that I made based on the system of The One Ring 1e a few years back, before FFG published their own TTRPG based on their Genesis engine. (Twilight Imperium is originally a 4X board game with a rich space opera setting, now in its 4th edition).
FTL travel is calculated in months, and space travel is based on the Journeying rules of The One Ring. This game assumes that the PCs are the commanding crew aboard their ship. In short:
- Player must divvy up roles among the PC aboard voyaging ships between that of Captain (or CO), Navigator, Security Officer, and Chief Engineer. There are other roles (Doctor, Quartermaster, Steward, etc) but they map with the four basic roles for the purpose of triggering hazards.
- There is a preliminary navigation roll that may make further rolls easier.
- Players must make spacefaring tests for each leg of their interstellar voyage (each role tests a different skill), accumulating fatigue when they fail.
- Special results trigger hazard episodes from a table. Hazards usually challenge all passengers, but sometimes single out a specific role.
- Some hazards test to avoid a negative outcome, some to trigger a positive one.
- The condition of the ship and perks purchased by players modify the accumulated fatigue and mitigate/worsen outcomes.
Similar to that, my Star Wars RPG (also based on The One Ring RPG, but 2e this time) has an Opening Crawl minigame where players "act out" the introductory text at the beginning of each new chapter, determining their conditions and dispositions as the game starts
in media res. This one is more about making an introduction than space travel per se, but it generally also imply hyperspace travel.