Scary part is that I had this exact idea yesterday. My plan was to create a graph where I can see all the possible "legal" transitions between board states.
However, upshot, taking account of the symmetries, this is doable on a single sheet of paper, though I'd suggest making the board smaller than you may initially think.
There is also an equivalent set of "worst" choices, and even for the "best" choices, it has four rotations, since there are four corners that X could start from that are topographically the same.
Still cool though :-)