No, because reason is based on the principle of non-contradiction. Anyone who makes a deductive argument must state their premises and how their conclusions follow from those premises. There are certain rules which allow you to make inferences from certain premises and if those rules aren't followed then the reasoning is invalid. Logic isn't some tool that you can bend anyway you like.
Agreed (although I think not enough information is available to us to construct fully reliable premises about the nature of God or His will, i.e., 1 Corinthians 13:12, which is why faith is necessary), but the implications of what I've said is that one of the premises of your argument requires that scriptures be taken out of context.
Your argument seems to be:
1 The Bible teaches that we should petition God through prayer
2 The Bible teaches that we cannot change the will of God
3 God responding to petitions requires that we change His will
Therefore it follows that either 1 or 2 is false, and we can dismiss one of them.
Without the third premise, the argument is not sound, and I would argue that the third premise requires that certain scriptures be taken out of context or dismissed altogether. Does the nature of God's will need to be fully explainable in order to follow what the Bible tells us is His will for us? Can we be okay with it if God's will is more complex than what we can understand? Doesn't the Bible teach that God is beyond the scope of human comprehension? Are you confident enough in that third premise to deny what the Bible teaches is His will for us?
The Bible is not a challenge to see if we can figure it all out or not. We have to be able to accept that there are some things that we can't understand, because God has seen fit to give us only partial information, for now. So we rely on the authority of scripture, since we don't have enough information to know if any premise
not derived from scripture is valid.
Maybe I could phrase it in another way: What do you make of 1 Corinthians 1:18-31? What about 1 Corinthians 2:14?