Zivanb : apart from young modules of Fat material .. do also try to lower the mass density.
Zivanb The BDF2 integrator I was using seemed to feel too shaky
Depending upon the shot dynamic and animation u can choose the integrator. I usually use BDF2 and TRBDF2 if the movement slow or Normal.. But if its very dynamics and fast i prefer to use Backward Euler. But yes it depends upon ur settings.
Do play around with "Initial damping" parameters of tissues , which are giving unwanted frequency jiggle.
Usually for fat tissue i do start with 0.5 to 0.8 initial damping.
playblast , looking nice ! Try increasing/varying pressure of fat , especially the inner layer of fat.
Reducing Fat's mass density and upping initial damping will definitly help a lot.
Also on the thigh muscles u can put some value in the initial damping parameters.