A couple of questions (one of them might be a solution to your problem):
- - Have you added keyframes for the surfaceTensionEnvelope and pressureEnvelope on the fat's zTissue node to create some runup frames?
- - Have you tried to lower the pressure and surfaceTension attributes on INNER_zMaterial?
- - Do you have collisionDetection turned on on the zSolverShape?
Looking at your screenshots I can see that the fat is exploding in the areas where you don't have any attachments, and the attached areas are more stable. If all of the above solutions fail you can always try adding attachments in these unattached areas.