I guess I'm going to have to give winning without Conscription a shot.
It is done. Took a few tries, but I have beaten the US without using Conscription. The pics:
Look at the prestige to confirm that this is the same game:
Taking Washington:
I then took Philadelphia and then Victory at Last:
Union Recognizes us:
I had to retreat from my first attack on Washington, but then I gathered enough troops to win easily on the second try and then onto Philadelphia. As said, the key is to be constantly converting POPs to soldiers so that you can constantly be recruiting new divisions.