Nathan, I agree with Keyur that you should initially work on a small piece of this.

I expect you are correct about the source of the problem. I expect those thin "petals" an important part of the model.

I can see that the sphere has not been sliced by the third plane.

In any case, if you want to share your model, you can right click on the Mesh and Clear Generated Data, then File > Save, then File > Archive and then you can attach the .wbpz file after you post a reply as long as the file size is < 120 MB. Say what version of ANSYS you are using in your reply.