Thank you for your responses and advice! I've gone through some other threads in this boards, as recommended, and it's been very inspiring. Especially Inspectre's alterations.
Although I agree that expanding the Gaedren business so the PCs have to work for it before facing him is the best solution, I don't want to create a whole extended quest before and after the Old Fishery. The reason is that while I can probably write a plot, I'm just terrible at creating creatures, and calculating CRs and all those things, so that's the area where I'm most likely to make serious mistakes and ruining things. So I was thinking about having a little pre-session heavy on the roleplay with each character, detailing how are they daily lives and how whatever Gaedren did to them has affected them. My players are very RP oriented (all three of them are party faces) so I doubt they'll mind waiting for a bit before meeting and getting their hands dirty if I do this.
As for the old man himself, I was thinking maybe two possibilities, depending on how they deal with him.
PLAN A: Gaedren manages to escape or is captured alive, and later becomes the Emperor of Old Korvosa. If he escapes, Kroft offers to use her resources to track him down as long as the party keeps helping the guard, as an additional incentive (just in case the money isn't enough to keep them together). She drops hints here and there about where he might be, until she finally pins him down in Old Korvosa, just in time for the people of Korvosa to burn down the bridges to the island for fear of the plague.
If he is captured alive, he escapes during the chaos resulting from the plague and ends up in Old Korvosa as Emperor. In any casy, when Zellara talks to the PCs at the beginning she is more interested in capturing him than in having him killed.
PLAN B: If the PCs manage to kill Gaedren despite my best efforts, they discover evidence that he was but a part of a bigger operation involving Devargo, who used Gaedren to distribute Shivers, smuggle slaves and whatnot. Once again, if they don't deal with Devargo for good, he ends up as Emperor. I just don't like Pilts very much (although since I have an actor and a bard in the party, if he's the Emperor I could substitute the blood pig thing, which I find pretty gross, for a snuff improv exercise or something like that).
As for the traits, I figured I only had to worry about the ones the players choose. Here's what I have so far.
-Hal-orc bard, CN: Missing child (missing son or daughter)
The bard had a little boy with a noblewoman a long time ago, and since the lady didn't want to raise a bastard one-quarter orc child, he kept him. Gaedren abducted him when he was ten, and it's been two years since then. The child is at the Old Fishery, but he's deeply traumatized and will run away with the rest of the orphans.
Assuming he isn't rescued then, the party will find him again during the riots (maybe with Amin Jalento and the angry mob). I know have an NPC to put in danger as often as I see fit. He can contract the plague and be trapped in Old Korvosa (since that's where the PC lives) when they destroy the bridges, or whatever I can think of.
-Human cleric of Abadar, LN, works as a lawyer: Framed (family honor)
The cleric became a priest of Abadar and a lawyer to help his loved one, but in the end it wasn't enough. The framed person was absolved, but now everyone thinks they're a murderer. They haven't been able to find a job ever since the trial, makes a living by leeching off the PC, and is in the brink of homelessness. Unless the PC can clear their name (which requires both evidence and the testimony of Gaedren or one of his thugs) or find them a steady job and housing, they will turn to a life of crime. If that happens, perhaps the person framed will be one of the captains of the Emperor. Or, if the framed person is a woman (the player hasn't told me the details yet), she could apply for a position in the Grey Maidens.
Of course, in the chaos resulting from the King's death, nobody has time to reopen an old case. Cressida Kroft offers to help speed up the process if asked, as long as the PC keeps working for her, but it's going to take some time either way.
The third player (human urban ranger, NE, works as an actor) hasn't told me yet which trait she's choosing so I have nothing.
I honestly can't tell if it's good or bad or convenient, but at least I came up with something and it's thanks to you people and this board, so thank you!