That's part of the point though. If there is such a god that is totally isolated from the Universe, the deistic variation, then his existence is inconsequential to us.
However if there is a god of the personal variety, which you seem to be addressing in paragraph 2, which interacts with the Universe we should be able to detect these interactions since they would violate the laws of physics. It's not that it would be reducible and confined to physical laws, it's simply that there would be obvious signs of these times when he does interact. Similar to when you toss a rock into a body of water, the entry creates a ripple effect.
But if God IS/ARE the laws of physics. Mind = blown.
You keep suggesting he has to operate outside the laws of physics. But if that IS God. Think about it, we are inherently obeying him and bending to his will, because we ALL have to adhere to the LAWs of physics.
Either that or an ancient alien.