Use the clipfactor entity attribute (increase it to 2-3 or an even bigger value).
Concerning dynamic lights I am sure that they get clipped correctly because I've made some tests about that a few years ago. However, it could be that more lights come into the view frustum (i.e. more than the shader supports) and thus the light priority changes and the scene looks different. Use the light count material to prove/ disprove that.