about the difference between the optimization goals "Planarity" and "TruePlanarity": There are slight implementation differences for these two goals, but in your case practically there will not be any difference. You can use either of them (both at the same time is ok but does not make sense).
The given geometry is certainly a challenge. You might want to try the following:
1) Pure planar quad solution: This is only possible if you stay close to the pattern of principal curvature lines. Try to use etExtractCurvatureLines to understand this pattern, and try EvoluteTools T.MAP.
2) As a last resort, a hybrid mesh will always work: http://www.evolute.at/?p=2008_Louvre