So basically - my Acolytes have figured out that the Alms House and the Chrurgeon is the source of the missing people. They have a non-aggression pact with Cord Luntz and his gang, who has hired them to take out the Churgeon.

They have not dealth with the "Enforcers" yet, who will move against them soon.

The group is going trying to foment a revolution and persuade the people to "rise up" against the Churgeon.

I am thinking of having this backfire in their faces as the Alms House is how many of the residents are fed.

This can turn ugly and the enforcers will then bear down on the Acolytes and the narco-gang. It is going to turn into an all out skirmish accross the district. 

The people, "enforcers", and other Logician agents will hunt the Acolytes down.

This will also set up the Chrugeon/Logicians as a recurring theme.

What do you guys think? How would you guys make EoD more interesting?

I recently played through Edge of Darkness which I just plugged in to my campaign. It fit in nicely as Edge of Darkness has a lot of potential loose ends which can be covered by your own in game conspiracy.

As for your specific question here is my advice.

• Don't just kybosh the plans of the acolytes. Getting the community to rise up and purge the evil doers is some thing Witch Hunters actually do in 40k so it must work some times. Use a yes-but strategy. Besides it's pretty inventive beyond just kicking in the door.
• If you still want things to have a chance to go sour make sure your players know the risks ahead of time. That some times these things can get out of hand. Their characters probably aren't stupid and before they start rolling dice they should know what the stakes are.
• If you use a yes-but strategy remind the acolytes of their specific mission. Which is to investigate. Frankly if they know about the Alms House and have reason to believe that a conspiracy is underfoot they've already finished the objectives which is to simply investigate.
• The specific yes-but I would use is to allow the torch wielding mob to be successful at claiming the Alms House and discovering the absolute horror within. However because of this the Churgeon has plenty of time to pack their bags and escape. In the after action report this could be taken negatively. The Inquisitor handling the acolytes might remind them to manage "appearances" that being that high profile cultists and the like escaping right under their noses looks suspicious. The Churgeon then becomes an aggravation for the acolytes. Only one or two scenes reminding them of the escape and how it looks should prompt the players to find a way to clean up this mess. Which could lead right in to another investigation. Player driven hook and motivation > Scripted motivation!