I think the argument was that God can interact with us in inexplicable ways. That God can choose to do something with no rhyme or reason other than it is his will. Such acts would be completely illogical with no pattern such that we could never predict such behaviour or write a rule for it other than "every now and then, strange things happen".

If God changes the laws of Nature once his 'program' is running, and the laws before, during and after the change can be expressed mathematically (logically), then there is no real difference between God changing them 'on the fly' compared to writing the more complex rule before starting things off. They are just two different ways of looking at the same thing (so this is really option 4 in my original post - again remember the question is can God interact with us in inexplicable ways).

Regarding the "almost anything is possible" I would postulate that your statement is true only within the bounds of the four options I laid out in my original post.