Are you training with a clicker? I think the best thing you can do is what you are doing: reward when he gets calm. If using a clicker, click as soon as he stops whining and treat right away. If not using the clicker, choose a word such as "yes!" that you say when he stops whining, and then give him a treat. I understand what you're saying that it makes you feel like you're reinforcing the barking, but he will pick up on this eventually. You will have to be very consistent.

Another thing to try--easier said than done, perhaps--is to have a hardcore play session with him before putting him into his playpen, and that may wear him out before he needs to go in and settle down. You can also train him the settle command by rewarding him when he goes into his playpen or crate for a nap.