Okay, tracking this behavior, it appears that:
1. ecommerce/register/index redirects to ecommerce/register/user-new via user-login.
2. user-login passes user_session_id to user-new.
3. user-new does not collect user_session_id (drops it) and subsequently the contents of anything already in the new user's shopping basket.
4. user-new-2 also does not collect or pass user_session_id. Upon post, user is redirected to an empty shopping cart and issued a new user_session_id.