God's omnipotence is stretched in time
You are absolutely right, Tom. God cannot contradict logic. And maybe law of noncontradiction is the single law which works even out of our universe. In the beginning of times when God have created laws of physics in our universe they already started to work and he couldn't cancel it or make anything contradict to these laws.
Many many years past before humans was created and God would be glad to make them once with knowledge of all laws of universe. But it was just impossible. Instead of it God made feelings and if human hear it and acts accordingly to it, he feels happy. But human is too limited in his mind thing. And he very prone to as I call it "last bit error". Human can fully rightly understand the situation but just in the last moment do false conclusion. It is always looks like answer on a question yes or no. E.g. in China they tried to kill all sparrows to save harvest or in Africa they tried to kill all elephants to save the soil from devastation. In both examples human made false conclusion about flow of process. Human still far from understanding all laws of universe. But some people already starts to understand more than other. When all people will understand his nature deseases and children deaths will be stopped but it will take time...