It seems to me this is cut from the same cloth as the various arguments that have been put forth through the centuries and grouped together as “ontological arguments.” The idea has been around at least since Anselm wrote it down in the eleventh century, with various refinements and variations rebuttals appearing since then.
Here, my reaction is that I would be reluctant to accept any argument that relies so heavily on considering what the human mind is capable of thinking about and/or understanding. For my money, the possibility of breaking an idea into “simpler components” speaks to nothing more or less than the current limits of human thought processes. I don’t know whether, assuming I were to set my mind to it, I could break down omniscience that way, but if I try and fail, I don’t know that my next-door neighbor Mary couldn’t blurt out an answer immediately. She might see some nuance that has escaped my notice. To be fair, I suspect you’re probably right, but I’m not sure that probably is good enough when the stakes are proving the existence of God.
Also, I would ask, What obliges me to accept omnipotence in particular as the critical defining attribute of God? What makes it both necessary and sufficient to declare an entity to be God?