The argument about omnipotence is not an argument about God. It is an argument about omnipotence, or indeed about a particular species of omnipotence, which we can dub "unlimited omnipotence". We don't need to get God involved at all. We can just as well assume any being that would be omnipotent in this sense and then argue that the existence of such a being makes no sense. The point is not about the existence of such a being, it is about the human mind. It is about the fact that the existence of an omnipotent being makes no sense to the human mind. Given this, it is up to each of us to decide whether we want to believe something that makes no sense.
I repeat the argument here:
Suppose a being is assumed to be omnipotent. He should be able to create a rock impossible to lift. Once he has created the rock, either he can lift the rock or he cannot. If he cannot lift it, then he is not omnipotent. If he can lift it, then he failed to create a rock impossible to lift, and so he is not omnipotent.
See? There isn't the word "God" there. The argument just shows that the idea of unlimited omnipotence is nonsense.
If god's omnipotence does allow it to violate logic, then a god can simply violate the argument that it can't be omnipotent, all benevolant and all knowing.
If we take omnipotence to be power without any limitation or restriction, then logic cannot possibly be a limitation or restriction to an omnipotent being, but this is precisely because of this that the notion of omnipotence is illogical and therefore nonsensical. You can always choose to speak nonsense but do not expect logical people to accept what you say. To understand what the word "omnipotence" means is to understand that the idea of the existence of an omnipotent being is illogical and therefore cannot make sense. You can always say "I believe in an omnipotent God", but you cannot make logical people agree that your idea makes sense.
It should be noted that this debate about omnipotence has been going on for centuries and still there are people to delude themselves that there may be something somehow that has not been understood about it yet. But no, the argument is very well-known and logically very, very simple and it has been discussed so many times that the idea that we may somehow all have missed a crucial point about it is total wishful thinking.