KinematicCharacterController gets stuck inside the collider when free falling

[VergilUa]

Got an issue with a following setup:

1. CC setup with collider set as cuboid;
2. Translation is set downwards (see as falling) and horizontal is set towards collider / wall;
3. CC gets pushed upwards only, instead of upwards and right (opposite side) of to depenetrate.
4. Which results in a CC getting stuck like so:
   

Zoomed in, it looks like this:

Any suggestions how to workaround this?

I've tried adjusting character offset to larger value, but that messes up the autostepping and still does not seems to be reliable enough.

[VergilUa]

For the future readers:
As a workaround, ended up writing a depenetration algorithm on X axis that applies opposite movement from overlapping hits from the edges of CC.

Still, would be nice to have an [optional?] CCD for the KCC.
As it seems to passthrough colliders and triggers / sensors with high movement delta / cc.translation.