This God is all-powerful, all-good, and all-knowing. He is an ideal Being, the answer to everything. This God's thoughts are always objective, never subjective
Then there is no case that can be built against God. The only way to do it would be to show that it isn't
1) all-powerful
2) all-good
3) all-knowing
The first and second are not easy to do, it is possible to show that someone isn't all-powerful, but God is too elusive for that kind of testing.
In order to demonstrate that an entity is not all-good we must also be all-knowing. Moral situations can only be judged when we have all the information that is required to judge it. We can have a good idea if something is good or bad, but sometimes our perspective makes it impossible to ever know.
For example, here in Manchester a man who was defending his home against armed burglars
ended up killing one of them and getting 8 years imprisonment. Given the information, a case could be made that the man was acting in a good way, self defense and all that. A little bit more information reveals that the man was a dealer, and was being robbed by rivals. As they were leaving he had a scuffle with one of them, stabbing him 4 times in the back.
It stops looking like a valiant homeowner defense situation and begins to look a bit more like a violent man seeking retribution for being screwed over by other violent men.
My point? Sometimes even a small amount of further information can radically change the morality of a situation. Since we are not all-knowing we cannot know if God is all-good. So in conclusion, this line of enquiry proves useless as a means to develop a case for the non-existence of the God you have described.