Cleverer blokes than me can explain the apparent contradiction to their own satisfaction if not to others. E.g. C. S. Lewis in "The Problem of Pain". Can't remember if your mate Polkinghorne had a go in the book whose name I've forgotten.
The brighter than any of those David Hume allowed (in his "Dalogue Concerning Natural Religion") that any amount of suffering [i]could['i] be consistent with any amount of power and love, but then this is just such a level of open-mindedness as you might expect from the man who denied causation at least in the logical sense: no number of B follows A observastions, or successful prediction of the same constitutes a final proof that the correlation inevtable.
In the Dialogues, Hum, arguing through his fictional surrogate Philo, doesn't claim that suffering disproves the Christian God. He argues in a different way: assume an intelligent moral being from a different universe were presented with ours, and informed of a single fact, namely, that this universe was an intelligent construct, what inferences could be derived about the power and goodness of the creator and the possible limits of either?
As a thought experiment (or as the Michigan pilot and old earth creationist - can't remember his handle - called it, I think, "ein Gedankenexperimente" - is that a real word, Khandro?), I invite anybody to answer Hume's question.