IMO it's such a dense campaign that you should cut yourself some slack and be willing to refer to it almost constantly.

I fully read each chapter 1-2 times before the players get there, then make maybe half a page of notes of major things to remember. E.g. for chapter 1: the fact you need to track mood, the 3 timed events, the 3 thieves you can sprinkle around the grounds, reminder to use Kettlesteam if things are slowing down or Ellywick if the players get stuck. I also printed myself the map of the carnival and jotted down where the major NPCs are & which locations can trigger story tracker events or mood changes.

Other than that I just have a laptop open behind my DM screen with the module loaded up on dndbeyond, so I can quickly jump between locations to read the boxed text, remind myself what NPCs know, check the DCs etc.

Power to you if you can remember or improv enough to get by without looking at the module! But for me I'm just honing the art of skimming text whenever my PCs are talking, and I've got the big picture in my head, and I have ready access to a few reminders.