I think you called it.... if I rest my thumb on the cylinder while cocking, when it gets to full cock, it is not fully sitting in the lock, almost, but not quite as it is just short.
Yes, the hand is the two stage style. Will replacing it with a new one correct it?
What fitting is required?
The hand will require fitting. It is not a drop in part. It's pretty easy to do but it can be tedious because you need to file a little and reassemble it far enough to check function then keep doing it until you get it right.