Bloodmoon:Supply Route Problems

Quick Walkthrough
#Speak to Falco/Carnius about your next assignment (whoever you chose to side with). 
#Talk to Falco to be informed about Baro Egnatius and his desire to receive extra payment for an ebony ore shipment. 
#Meet and talk to Baro on the docks in Raven Rock. 
#Return to Falco who will suggest to speak with Apronia Alfena. 
#Speak with Apronia Alfena and receive Elberoth's saber. 
#Speak with Falco again. 
#Return and confront Baro with Elberoth's saber equipped and readied. 
#Return to Falco once you've intimidated Baro to deliver the shipment without extra payment. 
#Return to tell Carnius the news if you sided with him previously.

Detailed Walkthrough
Carnius Magius
If you sided with Carnius you'll get this quest from him in Fort Frostmoth. He'll complain about getting things done and tell you to go speak with Falco in Raven Rock about problems in the construction. If you sided with Falco just go see him to start this quest. 

Falco Galenus
Speak to Falco to learn about the current problems in construction. Apparently Baro Egnatius has demanded a ludicrous amount of extra payment for the shipment of ebony ore he is supposed to deliver to the mainland. Falco wants you to have a talk with Baro in order to convince him otherwise. 

Baro Egnatius
Baro is down by the new docks in Raven Rock and seems quite adamant about being paid extra. Even a good deal of persuasion has no effect on him, but he will mention Elberoth, the late captain of the wrecked ship you found earlier in the Missing Supply Ship quest. Apparently, Baro doesn't know about his fellow captain's recent demise. Return to Falco with the news (ask him about extra payment again) and Falco will tell you to speak with Apronia about the matter, suggesting there is some way to exploit Baro's connection to Elberoth.

Apronia
Apronia, the lady you previously rescued from the lost ship, is located near to Falco. Speak to her about Elberoth and you should be able to easily receive Elberoth's Saber from her. Note that if she died previously, it is still possible to finish this quest by retrieving this Saber from her corpse. 

Return to Falco with the Saber and talk to him about Elberoth. He suggests that you confront Baro with the Saber since it doesn't appear that Baro knows of Elberoth's death. 

Confront Baro
Back to Baro you go, but first equip and unsheathe your sword. If you don't Baro will mention something cryptic about the saber and Elberoth, hinting that you should equip it and unsheathe it. Once you do, Baro will immediately recognize the saber and rather ungracefully back down from his desire to receive extra payment. 

Return to Falco/Carnius
Once you've intimidated Baro sufficiently, return with the news to Falco who will reward you with 1000 gold (if you sided with him). If you sided with Carnius, return to tell him the news after telling Falco, and you will receive the 1000 gold as well as 10 Cure Common Disease potions. 

Notes
If you didn't rescue Apronia during the Missing Supply Ship quest, Falco will suggest you look around the shipwreck site and see if there's anything you missed. Apronia's corpse doesn't disappear, so the saber should still be on her body if she died.
You can also kill or pickpocket Apronia to get the saber (if she has the sword equipped, you'll need to use a Disintegrate Weapon spell to break it and then pickpocket her).

Bugs
  This may also happen if your hands are readied for a spell, and may make him unwilling to talk, regardless what you do with your hands.
  You can use the Console code   to get past this and move on to the Apronia-related steps. 
 

Quest Stages