Alright final update for now. I've updated the project (same link)
wackytoaster.at/parachute/ceilingSlopes.c3p
I did add a velocity-based pushout that solves issue #2 mentioned above, but adds some other issues in that it sporadically does not work. So it's disabled in the project. It's kinda fun though.
Issue #1 cannot be solved as easily as expected, the issue is not that the jump isn't executed by the behavior, but rather that the pushout actually pushes the player into the floor and thus the pushout fails. I tried changing the players height slightly during the pushout to compensate but that also did weird things. I feel like this should work though, maybe I made an error somewhere.
Issue #3 is a bit more complex than expected, probably another can of worms that I don't wanna open at this moment. I had a solution that kind of worked but was framerate dependent, so... nah.
For now I'm actually fine with all these 3 issues being present (for my project). It's not make or break for me. But of course, if someone happens to find a solution for them, let me know.