A few ideas: - Hamlet does not view God as a loving and comforting God, he fears him and his judgement and believes in him whole heartedly. His beliefs appear a mix of both Catholicism and Protestant. For example a Catholic element is that Hamlet believes his father is in Purgatory, but he shows Protestant views as well. (this is a relection of the time in which most people held Catholic beliefs but were under Protestant rule)
Something else that is interesting to do with Justice is that Hamlet is possibly more concerned with Justice than with actual morality.
In act 3 scene 3 when Hamlet thinks that Claudius is praying. Hamlet oversteps the bounds of Christian morality when he decides that 'to take him in the purgin gof his soul, when he is fit and seasoned for his passage? No.'
I guess this shows that Hamlet is not always so moral afterall, but instead wants complete justice. This is perhaps a contributing factor as to why he wanted to be completely sure of Claudius' guilt. And this may be why he now decides to ensure that Claudius has the same hellish fate as his father. Although moral, it is fair and just.
Hope this gives you a few ideas :)