Ha ha, yeah it's all a bit silly but it actually brought me to some pretty profound conclusions. The short answer is yes, God can do anything. The explanation to how it would happen is a bit trickier. Here is my explanation stated in simple terms: God can do anything, and that includes changing forms. God can create the enormous stone in His omnipotent form and God can then change His form to one that is limited in power and then not be able to lift the stone that He Himself created.
It relates back perfectly to our discussion regarding God being all-powerful. If God is truly all-powerful, then He must also be able to exist in a capacity in which He is not all-powerful, otherwise He is not all powerful and is limited. But God is all-powerful and unlimited, so it must be that He can also exist in a capacity in which He is not all-powerful.