If you want to promote Elf to Commander, I think that's fine. She'll do a good job - better than me, for sure. She's earned it.
But she'll still be in your command chain. The flirting, like back on Mahuitalotu? That would be disastrous. You two can't date as Captain and Commander.
You're right. We can't
Of course, since you two will both be Commanders, you could date.