This looks like a problem with the collision thickness. There are settings for it on both the obstacle and the cloth (you already changed the self collision thickness, but there is also a setting for collisions with obstacles).
Depending on the scale of the scene, you sometimes need to lower the number a lot. I tested a similar setup and only got a similar glitch when the cloth was floating a noticeable distance from the obstacle. The collision distance (on both the cloth and collider) should be lowered to the lowest value that doesn’t clip. Also, adding more subdivisions to the cloth object helped on my side.
Blender’s cloth simulator isn’t quite designed to handle extreme stretching like that. This may seem like a simple scene, but it’s a case that’s pushing the simulation outside of its intended purpose.