Maybe it's just me, but I started a second run-through with the smaller base ship to see what changed and if it's actually moving any faster I can't tell the difference.
Also; after reading a few other people's comments I gave the autopilot a second chance and I think I may have just hit a run of bad luck with it, but now I have a different observation. It seems odd for the ship to travel faster with the autopilot; the mini-game punishes me for engaging with it when it should be rewarding me with getting where I want to go faster.
(Although in fairness I can't say that the ship taking longer to cross the system map while playing the mini-game isn't just a bug. Or possibly an illusion based on the time cycle counting differently while you're playing it, I did notice that the ship visually moves even faster under auto-pilot while you're sleeping.)