Hi Jimmy,
I am relatively new to groundwater modeling and FEFLOW, but I also understood Durchlassigkeitsbeiwert's response to mean increasing vertical discretization by increasing the number of layers. I believe you could use the 3D Layer Configurator to quickly add layers a set distance below existing slices.
For what its worth coming from a newbie, such as myself, to deal with the convergence issue, perhaps you could try blending conductivities between highly contrasting elements (i.e., in the new slices between your aquifer and aquitard near the contact, try setting the conductivity to half the difference between the conductivity of the aquitard and aquifer).
I have been trying to read up on the Van Genuchten method, would you be able to post a link to the Dirk Mallants document you mentioned?
Thanks,