I really like the game, great OST and it reminds me of the Made In Abyss anime, but what really bothers is the fact that the monsters keep respawning. If I die it's usually not because I made a wrong step or something but rather because I just can't kill the monsters as fast as they respawn. I just don't see any way to get past F7.

So I'd really like to see a mode where monsters are just on the map at the start, but once killed they stay dead. At least until I leave the floor.

I hear you.
One of the absolute blights on modern-day gaming, mindless respawn.
Although I do understand that some games depend on respawn for either length or difficulty (or both, most agregiously), I'm sure that by now experience on game developing and tools to do so must be enough to allow for at least a more clever or different way in which to treat re-spawns. Different monsters, different places, different numbers, with different intentions, etc. Variations of some kind, any kind. A single-player game doesn't need that frequent respawn, even for mindless grinding.
I figure it's time some developer re-imagines the way to do this.
:)