How to solve a sphere-mesh collision?

I play a game on wheels, and I can not get my sphere-mesh collision code to work properly.

Currently, what I have for the main loop (regarding the collision) is:

Calculate the player's acceleration based on inputs
Tightening speed to avoid clipping
Add speed to the position
Add acceleration to speed
For each solid object:
Check the collision for this object and solve it (the procedure is as follows)

If there were collisions:
Normalize the accumulated normal vector (explained below)
Slow the ball to account for friction

I've tried two main methods to solve collisions, each with its own problems.

The first method:

For each triangle:
In case of collision:
Correction of the player's speed along the normal depending on the distance
Accumulate the normal for friction calculations later
If the speed perpendicular to the surface is greater than the threshold:
Bounce off the ball off surface with damping factor
Otherwise, if you move to the surface instead of moving away
Clear perpendicular speed

The problem with this method is that when I hit a wall, the player will start bouncing erratically. The collision that I use to test this looks like this (player at scale):
Side level collision diagram, player at scale

The second method is similar to the first one:

Set the collision distance accumulator to an arbitrarily high value
Set the triangle's index to -1 (to indicate that there are no collisions)

For each triangle:
In case of collision:
Calculate the collision distance
If this distance is less than the value of the accumulator:
Set the triangle index on the current triangle
Set the collision distance accumulator on the current distance value

If the index is not -1 (there was a collision):
Correction of the player's speed along the normal according to the distance in the accumulator
Accumulate the normal for friction calculations later
If the speed perpendicular to the surface is greater than the threshold:
Bounce off the ball off surface with damping factor
Otherwise, if you move to the surface rather than to the outside:
Clear perpendicular speed

This corrects the problem of stiffness, but I can now move partly on surfaces supposed to be solid.

I do not know where to go at this point. I hope someone here will be able to give an overview of what is going on.

[EDIT] I can add videos if it helps somebody.

[EDIT 2] Here is a link of a video using the first method:
https://drive.google.com/open?id=1n1MxTYQkzKA2eixTkEOD3E7eOd0Ryl4f