Here's another trick. Inside the cup, the occlusion is mostly from the ball. We can use this knowledge to create a little fake Global Illumination. The ball is red. Where the ball is very close to the cup, the AO will go dark. Use that info - add some red to the shade of gray on the Blender Input_1, and connect it to the cup's Diffuse_Color instead of the Diffuse_Value.

Now the cup is red where the ball is causing AO.

Unfortunately, we're also getting red AO on the outside of the cup. The way to handle that is to edit the cup's material zones, using the Group tool, so that there is an inside material and an outside material. You'd then be able to use the gray+red only on the inside, leaving the outside still plain gray.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)