We did a little further analysis of possible problems. To put it up front, we still do not know how to really improve the situation, sorry.
By some hardware analysis (which involved taking apart devices etc.) we found that at least the antennas (yes, L13v2 and L15v3 do have two) are not the issue. The antennas are placed in the display hinge bar where the kill switches are located also. Replacing these with other antennas or changing their position did not improve the situation.
We also have the suspicion that the reception quality is fine but that the problem might be related rather to the sending path.
We are investing further, stay tuned!