As a lazy GM running CotCT, these threads have been lifesavers, as such, since I just finished running Seven Days to the Grave and I'd like to share what worked and what didn't work for our group in hopes it helps others run this part of the adventure.
The plague timeline: I had a hard time letting enough time pass for the disease to propagate after the Soldado encounter, mainly because I read the concerns about the timeline in this thread one session too late. I managed, but as a heads up for other GMs, make sure you have some filler beyond the Trinia encounter to have enough time pass. Ideally, you could have the PCs escort Trinia all the way to Harse, while having a short adventure or two in either Harse or Palin's Cove. You can find some information about Harse in book 3 I believe.
"Too busy" tagline: In many parts of this adventure, its assumed that the PCs will investigate the plague of their own volition, or have some of the encounters be assigned to them by Cressida or Ishtani. Also, it is assumed that any attempt to get help from any officials will be met with speeches about being too busy. This didn't sit well with my players, who were dumbfounded that Ishtani said he'd heard of someone selling a cure to Blood Veil in the Heights but was too busy attempting to cure Blood Veil by other means to go investigate. I tried to remedy that by having Ishtani not put much faith into this supposed cure, but that just got the PCs disinterested in the place.
Most importantly, when the PCs finished exploring the shipwreck, they felt that the evidence they got was so damning that it would have been unthinkable for the Field Marshal to say she was too busy or couldn't spare the men to investigate the Queen's Physicians. The PCs headed straight to the Citadel to present their evidence to Kroft. Thinking on my feet, I had the guards inform them that the Field Marshal had gone to a meeting with Dr Daviulus at the Hospice. She stomped out of the Citadel, brushing aside her guards and didn't seem to be in the best of moods. The PCs concluded that Cressida must have discovered something and went to confront the doctor, which may put her life in danger, so they dropped everything and rushed to the hospice looking for her. That made them want to clear the whole place with haste, which they eventually did. In truth, I'd decided that the Field Marshal did indeed demand to meet with the doctor at the hospice, since she just finished reading the end of week report on the disease and found that things are getting much worse, with the physicians seemingly ineffectual. The doctor dodged the meeting, pretending not be at the hospice, so Cressida went looking for him at the palace instead.
Shipwreck: My PCs were also surprised that no one had gone to the shipwreck in all the time it sat there till they got around to it. They found it hard to imagine that none of the churches could spare a cleric to take a quick dip and look around for the cause of the disease, since the ship was toted as the cause of the disease by many factions. They were also questioning about why such incriminating documents were left here this whole time without someone in this big operation sparing the time to remove them. I suggest making a small tie between the Sea Hag and the Red Mantis by having her go to the ship as per their request to clear whatever is there, but instead liking the place and taking up residence. The attraction of the wreck to the hag is that many people did indeed attempt to investigate, including clerics. More fodder for her.
PC death at the temple of Urgathoa: The encounters here are nasty, and wore my PCs down enough that eventually, we lost one PC at the Lady Andaisin encounter. Although there are many ways to bring in new characters into the story, I felt it noteworthy to mention that even if resurrection is very rare, going to the church of Abadar with the notes to a cure for blood veil as barter for a resurrection seems like a fair exchange.
