I don't think that the navigator + stay on target works as you think it does.
Both have the same wording:
"When you reveal a maneuver, you may rotate your dial to another maneuver with the same bearing."
“When you reveal a maneuver, you may rotate your dial to another maneuver with the same speed. Treat that maneuver as a red maneuver.”
which you can translate as:
"When you reveal a maneuver, you may rotate your dial to another maneuver with the same bearing (as the revealed maneuver)."
“When you reveal a maneuver, you may rotate your dial to another maneuver with the same speed (as the revealed maneuver). Treat that maneuver as a red maneuver.”
You may use navigator after stay on target but the reference maneuver that triggered its use stays the same.
So with navigator + stay on target you may rotate your dial to another maneuver with the same bearing or the same speed, which is already powerful, but it's not exactly chose you maneuver on activation.
Your translation is putting in a defining descriptor that is not there.
While I don't necessarily disagree, I would note that in most other cases where 2 things occur at the same time the player gets to choose order.
The most recent case of there being a defined limitation to actions/triggers that occur at the same time is the FAQ ruling on Advanced Sensors and Cloaking. While the reason/cause for the ruling is still a bit fuzzy, one word seems to define it, "immediately". Indicating that the presence of that word indicates special treatment or exception to "player chooses order" standard.
Since both those cards do not have the work "immediately" and I am not aware of any other order limitation to the specific "when you reveal a maneuver..." I would at this time rule that both are allowed in any order the player chooses...
I could see it ruled your way though...
Now the idea that using Stay on Target first then navigator to negate the red is interesting...if you need to go in the opposite direction...