Here you present two possibilities -- inclusion of the ability to violate logic and its exclusion.
Are you sure you know all the parameters of every logic?
Can I ask you this question: "In this inclusion, why did you not include the ability to create an experience of it (inclusion of logic)? Similarly, in the exclusion, why not include the ability to create an experience of it (exclusion of logic)?"
If so, can all experiences regarding logic (or violation of logic) be treated as a part of omnipotence?
When one tries to separate the attributes we don't know that we forget the consciousness (or the coordinator of those attributes) behind the attributes. If so, who must be that coordinator? I hope you will agree that this is another reasoning/logic.
So, IMHO, with our limited logic it is better that we do not blame it on God or His attributes. I think you didn't focus on the term -- 'omnipotence'.