Here are my rantings. Most of these are applicable to any campaign, but I think their worth emphasising if you're aiming to complete the whole thirteen-book AP.
Check player expectations
The longer the campaign, the more important this is. Check what your players expect, what they find fun, and what they are comfortable with. I did this through informal conversation and/or a survey. For example, do players enjoy the historical context of the setting? Do they enjoy combat? What do they find
uncomfortable? Would players dislike seeing or executing violent interrogations of criminals? How comfortable are they with mentions of sex (e.g., Rock Rackus)? Do they want mental illness and fantastical 'insanities' in their game (e.g., Distant Madness)? This can help you figure out what to skim over (for my game, this is Rock's fey orgy) and what to avoid entirely (e.g., for my game, the RHC forbids violent interrogations, bar the most extreme circumstances).
Identity
Identity is a crucial part of human experience. As such, an understanding of character and party identity can strengthen immersion and enjoyment. As mentioned by others, try to rope player-specific NPCs and quests into the campaign. On top of that, consider...
Backstory
If the party are constables (which I do encourage) and your players are writing a backstory for their characters, ask your players to include a reason for
why their character joined the RHC. What is their motivation for their work? After all, they will need to defend themselves from Dockers who denounce them for their service to the status quo.
Give players and characters alike an opportunity to reflect on their actions and intent. Be it in a quiet room on the RNS Impossible on the way to Axis Island in Book 1, Stover Delft asking the PCs to explain themselves, or a small NPC interaction that acts as a microcosm or allegory for the players interactions, the players and characters should be provided opportunities to reflect on their actions. Gray shades of morality color the AP and, likely, the party. Try not to make your players feel naughty word for their decisions, but rather, an acknowledgement of imperfection.
Understand party identity. Are they party government goons who solve crimes with their fists, savvy investigators with an eye to detail, or paranoid policepeople who never trust their eyes? Does the party feel over their heads when handling matters of international diplomacy, or do they see those in powers as untrustworthy or foolish? Keep track of your party's identity and play into it. It's okay to make your players feel uncomfortable at times, as it gives you an opportunity to relieve tension.
Understand character identity. Similar to party identity, but acknowledge each player has their own motivations and thoughts. I recommend trying establishing each player as a face for different groups and NPCs. Give every character an opportunity to shine and show off their expertise. In other words, try to make the default 'party face' change depending on the NPC's associations. For example, my game contains a well-dressed ghostspeaker who faces for The Family and nobles, a Vekeshi mystic, stolen by fey at birth, who faces for strange creatures and mystics, a technologist who faces for engineers, academics, and the Ob, and a gunsmith who faces for military personnel.
Reward roleplay. Reciprocate roleplay with roleplay. I have a 'pebble system' in my campaign, where players who roleplay their character well are rewarded a 'pebble' by other players. This pebble acts as a token that may be expended for a roleplaying opportunity. Examples from my campaign include, creating a rumour to catch that causes confusion around Steelshapers title (or was that Bronzebender...or Tintickler?) and laying a deceased druid to rest by summoning a bed of flowers.
Shared notes
As mentioned above, having a communal pool of notes can help players keep track of all the NPCs. Each of my players have their own notes, but they also have a communal Trello board, introduced in Book 2:
Recaps
Given all the moving bits in the campaign, I recommend recapping the previous session before playing a new one. Each week, I ask a player to write a recap for the session. That way, players can express their own views and hunches.
Feel free to use the forums
People here are friendly. If you have any question on the setting or want other's opinions, all you have to do is ask. You probably don't need this advice given you started this thread...
Investment
My philosophy to DMing is to show high investment in the world and campaign, provide opportunities for players to invest themselves in and out of session, and if they do, reciprocate their efforts by including their work in the setting or campaign. For example, for my campaign, we have a Discord channel used for between session text roleplay. I ask players questions each week about their characters (to encourage reflection). Players know that their answers are used to flesh out the story and create NPCs. Between books, or whenever characters have downtime, players may message me telling me what their characters would pursue by themselves, and I will reply with text responses.
I show my own investment by trying to prepare for fluid sessions, as well as creating various handouts. I'm not particularly good at making handouts and I don't have the largest repertoire of voices (As an Australian man, there is no way I can adequately voice the gentle French voice of Gale), but I try not to let these things preventing me from putting myself on the line. After all, if the players see you doing things that are initially uncomfortable but enjoyable, they too may join in.
All of this is limited by time. But if you are looking for what you can do in-between sessions to improve your campaign, I do recommend it. If your interested in any of these ideas, I can provide more specific examples.
Overruling philosophy
At the end of the day, you and your players should be having fun. Do what will facilitate that. If any of my or other's ideas don't feel like they would be fun for your players, don't feel the need to run with them. Though, don't be afraid to give new things a try. For example, I didn't think my players would enjoy the investigation aspects of book 2 as much as they did.
In saying all of this, the very fact you started this thread shows that you and your players will probably have fun.
Good luck out there, let us know how it goes!