1) Reveal Maneuver (say a straight one)

2) Change the dial with Stay on Target to a hard one (now red)

3) Change the dial with Navigator to a hard three (This now not being changed to a red by Stay on Target).

Would this be correct? So you would be able to choose just about any maneuver on the ship after revealing, and if it is of a different speed, without stress as well?

FAQ says no:

Stay on Target: "Even if the chosen maneuver is changed by an ability such as Navigator, the maneuver that the ship executes is always a red maneuver."

Stay on Target + Navigator pretty much lets you choose nearly anything on your dial, but Stay on Target will always make it a red maneuver, even if it's used first.