I think that Schellenberg's idea of the meaning the word "God" with a capital "G" is one which has the core characteristics of what Christian theologians consider the Christian God to have. Philosophers in their writings about whether or not God exists seem to be fixated on that kind God, and give very little consideration to the idea of a God who is not all-knowing or or not all-powerful or one who is evil. They also seem to give no consideration to the idea that polytheistic types of gods might exist.
I agree that this is how most philosophers depict God. The reasons for which are independent of anything the bible has to say about God. The bible just happens to describe God in similar terms.
Still all you can claim is because you haven't been personally convinced of God's love for mankind, despite the christian claim that he died for mankind, you don't believe he exists. It is not that there isn't any evidence, it is more that the evidence people use doesn't convince you.
These guys below would argue that the defeat and withdrawal, of the mightiest military force on planet earth, from their holy land, is evidence of God communicating his support for their Jihad.
If God is all powerful, all knowing and all evil it would solve your problem of why he seems to be a crummy communicator and thankfully so. However, It would leave you with a different set of problems, which is why many philosophers don't characterise God as evil, as you pointed out.