It's very Raidy-ish, without the most tedious part of that game (the grinding). The design makes sense and it's simplicity at least thus far is a pleasant change. The points above made by Ren I agree with, but a suggestion that may give the game some -oomph- would be a multi-level boss-scene before the game over / floor punishments.
I don't speak for everyone, but one of my favorite parts of the Ouka series of games was the gradual progression as you lost to the bosses. First time she hates it, second time she's starting to enjoy it, and by the third she's completely broken in. It would certainly take quite a bit of writing, and quite a bit of effort, but I think the framework is already there. The titles are unique and you could tailor the scenes to match the floor's theme, and write alternative events for losing to normal enemies while under the new name. This would add quite a bit of content; at least text wise, and would help justify the price point, as it is a bit steep.
Again, just my 2c; I'm barely making it through the first floor so far. But so far looks very promising!