Tonight, Alex was better and I think we gained back about 1 step of the 2 we took backwards yesterday. Lunging was much more calm, except for cantering to the left where I think he was panicking about falling and so kept throwing his head and fighting the lunge line. With time he finally went relatively calmly, so I let him change directions and he went really well to the right. At the mounting block he was a little impatient, but eventually did allow me to put my weight in the stirrup. He's not too keen on standing around a long time afterward though :-) This biting thing has to stop though... I've gotta get tougher about that.
Perhaps tomorrow, we will start to the right, and maybe he will be a little more relaxed by the time he has to go left. I only want him to have good experiences... that always has to be my goal, at least in these first months together.