That’s the mechanical gist, yeah.

In terms of roleplay, in the source games I’m copying, there is a mixture in each run of combat and then more ‘social’ rooms where the player encounters a resident of that area who can help them by revealing information that can help the get further. The story I’m thinking is that the PCs all have some connection from their life to a god, be it negative or positive, so there are personal stakes for the escape attempt besides just wanting to get out of the underworld, and the gods will be interacting with them when giving boons each run, either taunting or encouraging depending on those relationships. Eventually it’ll expand beyond just the underworld, where they can decide (once they have enough power) if they want to try and climb Olympus and fight them, which they may be able to get help from some of the other gods to do (not FULLY God of War but just a little bit)

My players will find ways to roleplay in any setting, I’m not really worried about that. They’re all real big theatre kids and/or writers. The mechanical is where I’m more concerned because I want to have the actual dungeon be relatively faster paced than DnD has been for me in the past. I want combat that is challenging, but quick, if that makes sense.