An incoherent triad

Believers often look at the atheist demand for evidence, as presented by typical atheists, as a shell game.

 I went over this issue with the link to Shadow to Light, but I want to pursue the same argument in a different way.

The question I want to pose is whether these three positions can be held in a simultaneous, coherent way.

1) Belief in God is not justified unless there is evidence for belief in God.

2) Evidence for belief in God is possible. There are things God could have done, and should have done, to provide evidence for his existence. Thus, the absence of evidence is really evidence of absence.

3) God of the gaps arguments are wrong on principle. If we lack a good naturalistic explanation for something, an explanation in terms of God will not increase our understanding of it.

If God provides evidence, no matter what he does, it seems to me that 3 could be used to dismiss the case for his existence. Thus, it seems to me that you can't hold both 2 and 3 together. One of them has to go.