Very complex objects [or meshes] can splat.
Have you tried splitting the object to be draped into a few grouped parts with less geometry and then doing them in turn...
Also avoid nested 'containers' inside the draped object.
My SuperDrape tool will also drape faces inside a selected group onto the mesh in another group, using somewhat different methods.
The advantage of it is that the original materials are transferred for each of the newly 'imprinted' outlines...

