I was in the middle of THE HOUSE ALWAYS WINS, IV and HOW LITTLE WE KNOW. I talked to the Receptionist, then to Cachino, then to Troike, then to Big Sal, then to Troike again. He gave me his thermite to destroy the guns in the basement. I went around the room and kept placing it wherever it indicated it could be placed until it said "Thermite removed," but the Quest is still telling me to use the thermite. Broken. Part of the Quest is also telling me to talk to Clanden, but after I tell him that Cachino sent me, there are no additional dialogue options, and he's still marked as a Quest target. Broken. I tried to find a solution for about an hour until I finally shot up the place and made them hostile. HOW LITTLE WE KNOW failed, and THE HOUSE ALWAYS WINS, IV told me to return to Mr. House and tell him that Gomorrah is hostile to me. Guess what? That failed THE HOUSE ALWAYS WINS, IV!

I made Troike place the thermite. Then I had a meeting with Big Sal where I made Cachino shoot him. Quest finished.
 
As for Clanden, I think you'll have to find something or talk to someone to initiate more conversation options.

Hi, I've also got this quest broken, but in a different way. I started doing the Wild Card: Side Bets quest, and got to know the Omertas. This meant getting past the dialogue with the receptionist, and I'm currently to do two different quests for them (one for Clanden, one for Troike). The problem is thatwhen I try to do the House Always Wins IV quest, the quest marker is for the receptionist, yet nothing I can say to her advances the quest. For reference, my Speech skill is 100, and I don't remember failing a speech check the first time.

Cachino's already dead in my game, Button Man capped him. Do I just need to do the Troike and Clanden quests to assess whether or not they're a threat? Because I don't dig chlorine-gassing dudes, but I guess if I have to do it, I will.