Stuff like FTL and “The PIT” doesn’t fit super well into your categories I feel. I think they’re a little to defined and narrow.
I think one way to slice it would be how the games handle progression, is there any? Is it only on complete runs or also on partially complete runs or every single run you gain something?
It’s similar to what you’re on but a bit more concise. So
No progression: the game is about completing a run, which is very challenging but also very rewarding.
Some progression: the game builds over multiple runs offering different/new ways to tackle it as you complete runs or discover stuff.
Full progression: every run builds on your previous runs.
I don’t see the point in naming a genre for rougelike card games. To me it’s a mash up between a full progression rougelike and a card game, and it doesn’t need a name. Also a name for rougelike with safe havens seem weird as well. And rougelikes with full progression by nature become grindy since that becomes one way to win.