Realistically speaking, the only reason that we should be worried about sticking around is reinforcements. Our PC is more than capable of handling the enemy fleet if need be.
This is flagrantly false. While in most other respects your analysis was on point, it overlooks four things.
One, we'd be attacking with two ships. Two, we don't captain both. The other ship can afford to take a few hits from the skiffs, but if the battleship sneezes at it, it will die. Or surrender. Statistically, it would get picked apart by the multi-attacker penalty alone.
Three, while you are correct that we could probably take on their entire fleet with just the defenders, that is not the case if they have heavy defenses. Remember that pirate base? How durable the dang thing was and how many rounds it took to destroy when backed up? That is what we would be in for. These defenses would be shooting at us every single round of combat.
Four, the enemy Commodore is going to remain under the cover of the heaviest defenses despite heavy pressure to mobilize. He's either cowardly and stupid, because this is going to bite him in the ass, or he's smart enough to realize the situation he's in. Him having good strategy and tactics would be enough to flip the delicate balance required for the Endeavor to solo everything.
Now, maybe,
maybe, we could survive that and win. However, even my best hope for the fight would have us losing the ship we bring along, damaging the Endeavor, and lacking the capacity to enforce our demands with limited marines, crew, and ships. On top of that is the looming threat of NASP reinforcements when their money maker is attacked.
[X] Demand Tribute. Demand that the local citizens surrender then pay tribute, loading all available shipping with high value manufactured goods before sending them up into space with sacrificial crews. (Time taken and yield variable, depending upon Diplomacy and Subterfuge rolls, in the range of 5-75 Wealth)
[X] Return Home. You have achieved your goals, return home with your prizes and/or loot.
The knock on consequences of slaving make me adverse to it.