I always approach Pen and Paper RPGs as interactive storytelling, where combat, investigation, and puzzles are all just plot elements. The characters are who actually tell and create the story, USING those elements-- Or not.
I get what you are saying-- The way the game is structured mechanically, investigation is demanded-- but that is again, a fault. Perhaps an unavoidable one, but still a fault. It leads to formulaic and inescapable/fixed outcomes. It is important to remember that the cultists are going to do what the cultists are doing, regardless of the involvement of the PCs. It is also important to have the NPCs do things as consequences of the actions of the PCs, that radically alter the script.
EG-- Say a PC notices the "Creepy as fuck, but TOTALLY AWESOME bookstop" when they stop in at the mansion, say through a roll for observation after saying they "Check the place out"-- The "bookstop" is really the ritual focus idol used to contact the great old one involved-- say, a cthulu bust. He does not know jack shit about Cthulu, does not care. The bust is cool looking, and would make an awesome bookstop for his book case, and "This rich bastard will never miss it anyway.", so he nicks it. He causes no other commotion when at the mansion-- Again, he stopped in to use the phone to find out where he was, so he could drive home. He leaves the mansion after getting directions, (The rich guy getting ready to do the ritual just wants him gone, so he doesnt EFF up the ritual, and the most expedient way is to send him packing in a normal fashion), but then when he turns around, the idol is gone. BOOM-- Plot derail!