Looking at what other dedicated finite element visualization software is doing with symmetric quad data I found that they seems to split a quadrilateral into four triangles (instead of only two). It involves creation of additional node at the quad centroid (sum of x coordinates / 4, sum of y coordinates / 4, value at the centroid sum of values at nodes divided by four). I include here two python matplotlib scripts which illustrate this procedure.
quad_2el_paraview_quad22tri.py (1.5 KB)
quad_2el_paraview_quad24tri.py (2.7 KB)
And below are the plots they are producing:
Perhaps in Paraview this kind of internal splitting for quadrilateral can be applied?