Expanding the focus a bit on the entire fleet could help--even if it's just in the form of hearing in passing dialogue more about other ships elsewhere that were able to save this or that--so that it doesn't come across like only the ship we're following is the only one that can do anything.
Word. That would completely fix some of the mildly eye-rolling moments when the trope is overplayed.
I know I said this "we're the only ship in range" thing was the worst, but I was being hyperbolic. Sometimes it's okay, sometimes it just leaves me scratching my head and thinking, "Really, now?". A throwaway line about other ships would just do away with that problem entirely if the hero ship has to be the one speeding off to the rescue.