I'm thinking that there may be a way to reduce that further if you consider symmetry/rotation or don't care much about the sequence, e.g. selecting any corner o

I'm thinking that there may be a way to reduce that further if you consider symmetry/rotation or don't care much about the sequence, e.g. selecting any corner or edge on the first move is equivalent and since we know that the first move must happen we only need less than 2 bits (2 at most) to encode the first move i.e. 3 states: corner, edge, or center.