When meshing challenging bodies, it is sometimes useful to slide-and-dice bodies in SpaceClaim via Split Body and Share Topology to isolate the trouble spots for tighter controls. In Mechanical, the bodies could be individually meshed in the 'right' sequence such that key features are respected.
Figure 1: Generate Mesh on Selected Bodies
This is done by first selecting the Mesh object in the Outline. Right-mouse-button on the body, then Generate Mesh on Selected Bodies. This was done twice to generate bodies shown in Figure 2.
Figure 2: Individually Meshed Bodies
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