Unity Generating PolygonCollider from mesh

Question

I generated a procedural mesh using marching squares and the MeshFilter component (it's 2 dimensional). Now I got the point that I need do collision detection with the character (a sprite with a box collider).

I tried simply converting the mesh's vertices to Vector2s and putting it inside the collider the following way:

PolygonCollider2D collider = chunk.gameObject.AddComponent<PolygonCollider2D>();
List<Vector2> points = new List<Vector2>();

foreach (Vector2 vec in vertices)
{
    points.Add(vec);
}
collider.points = points.ToArray();

This almost worked, but it had some flaws in the collider:

Then I tried to use an EdgeCollider instead, but this made the character jitter. Lastly I tried to set each shape coming out of the marchingsquares algorithm be a separate path, but this was somehow very slow.

Is there any ways to create a good collider for a procedural surface?

Edit: Edge collider approach as requested (I got a bit further with it in the mean time):

So, to implement the edge collider, I changed my marching squares algorithm a bit, so it can output pure lines instead of actual triangles. The problem with this was that at some points, the character just randomly goes into the collider: