Am I missing something? At the end of Escape from Old Korvosa the main escape route after Arkona Palace is to kill the giant reefclaw and escape on the barge. But isnt' the river being patrolled by Gray Maiden ships?
Although Endrin Island is under quarantine, it is not impossible for characters like the PCs to get on or off the Island, either by crossing in secret over the Narrows of Saint Alika, or by using the river.
Yes, the river is being patrolled by Gray Maidens, but there are probably not a lot of patrols on the water, since the maidens are not at full force yet and other places demand more attention (including the Narrows of Saint Alika and the one remaining bridge to Old Korvosa).
So, if the PCs escape via the river, they might notice one ship patrolling somewhere on the river, but that shouldn't be a problem for them.
I had the Arkona palace flood with Gray Maidens as the PCs left, explaining why there were so little in the water.
But then again, my PCs were openly antagonistic to the Queen.