First of all, totally not complaining! I think I uncovered a bug in the logic. Going to be very detailed since I don't know what aspects of my game specifically led to this. My rogue (who is a former street urchin and is aquainted with Nel) asked Nel for a bowl of soup, Nel gestured her to the chest. She attempted and failed once to open the chest. I told Nel to go eff himself when he asked for gold and retried and then opened the chest. I equipped the +2 longsword straight from that menu on another character who was close by without the closing the menu (I put it into the rogue's inventory and then transferred it to the paladin. Then I exited the menu and Nel still had a dialogue option. So I got curious and paid him a gold and was able to once again attempt to lock pick. It failed the first time, so for science, I paid 5g. And boy did that pay off. I opened the chest and behold ANOTHER +2 longsword. They are now both equipped and I have a very happy paladin and ranger.
I have absolutely no idea which of these variables led to the game allowing me to open the chest again, but I suspect it's because I said no, then successfully opened the chest and then was able to talk to him (the chest was locked again even in the cinematic when I spoke to Nel) the second time. Sadly there will be no third +2 longsword. :3
UPDATE: They both tragically disappeared when I turned in the quest.