PotA is an entirely different campaign with a much different structure. In fact, it barely had any structure at all other than, "this is an adventure location," and "this is another adventure location." It was about as modular as you can get.
You could do the same with SKT since it barely has a plot at all and what plot exists doesn't even make sense. But you couldn't do the same with OotA or CoS. They really require the DM knowing what's coming and the overall plot and structure in order to do it justice. Otherwise, the players will be just as confused and misinformed as the DM. ToA is the same.
Which is about all ToA is as well. Been running it for past 3 sessions without too much pre-reading (made up a rough plan of areas I want the pcs to discover, we aren't running it as a hex crawl, no interest in those these days) and have a good feel of the campaign- and am adding elements of the original Dwellers of the Forbidden City, and changing things up and inserting it in the Amedio jungle in Greyhawk.
My pcs range from 4th (new replacement for retired pc) to 9th level. I started to foreshadow ToA with 2x pcs starting to lose hps while on an unrelated adventure. Players stopped adventure in its tracks, headed back to town, consulted with various churches and a sage (Syndra) and when they learned the curse affected was only on people who'd been raised from the dead they really took an interest. Next thing they knew they were teleported to Nyanzaru and started to explore the exotic city. One pc had a dream of a skull floating over a city in a jungle caldera so asked questions about this and started to hear about the fabled forbidden city.
Session 2: Spent exploring city, learning rumours, meeting with merchant princes and interviewing all the guides. As their is a ticking clock for 2 pcs they are keen to get to Omu ASAP. Chose a guide, go some advice from them and then figured out possible path to fly to the city and started following the river Soshenstar. (They are flying 40 miles per day). Located camp Righteous, camped nearby and encountered some herbivore dinosaurs (avoided) and undead dinosaurs (which attacked their camp).
Week 3: (Last night): Decided to explore Camp Righteous. A torrential rainstorm had started early in the morning so nobody got the benefits of a long rest, was windy and rainy all day so sought shelter in the camp (followers of Heironeous in my campaign). Found shelter and spent most of the session exploring the House of the Man and Crocodile (without a guide so no idea of background) but eventually overcame all the traps and gained the rewards- my guys really enjoyed this one.
Headed south and located Camp Vengence and met with the followers of Heironeous and the unhinged leader of the group (think Colonel Kurtz in Apocalyse Now), some role playing where he ignored their demands of their own important mission by ordering them to clear the jungle to to north of undead and reopen his supply lines. Nodding their heads dutifully they agreed but are going to head south ASAP instead realising he is a complete nutter.
So 3 sessions in, my guys really have a sense of urgency with this one due to the hp loss they are suffering and are keen to get to the meat of the adventure but will have 2-3 more encounter locations they stumble across first.
So AFAIK this is no different from any of the other adventures form WoTC for 5e. The background etc is easily ignored/modified to weave into an ongoing story, and I never follow the plot as written, instead choose locations and adventure sites that meet my interest or my players, plenty of the others can be dropped into other campaigns in future.
Stormdale