The best way you can help Alyssa feel better is to do your best to be strong and reassure her that "all the other kids are learning how to enjoy being here too". Ask her who she likes to play with and what they play. (You might not get much back, but Who Did You Play With? is more helpful than 'what did you do?' )
I wouldn't put pressure on her for good behavior, because crying isn't being bad. She's signaling her sadness that school is not the same as she left it, and so something which should feel familiar feels unfamiliar. I'm not sure that focusing on behavior will help her feel better. Could you imagine a situation where you were upset by a tough transition and someone decided to bring it to your attention that they were going to be monitoring your actions and attitude? I'm not asking this sarcastically, either... it would only add stress.
Instead of rewards, consider spending a few extra minutes just snuggling, reading a book, or join her for a few minutes in something she likes to do. Sometimes, when my son is upset about something, spending five minutes to work on building something or play gives him validation that even though things are changing, I still love him, and he can be secure in that.
There's another technique a mom blogger suggests, and I have used this with my son a lot. It's called a Boring Cuddle. This works well for kids who are upset about things that we either don't think need fixing ('that's not fair') or simply can't be fixed. link to that:
http://kloppenmum.wordpress.com/2010/12/06/boring-cuddles...
Ask the new teacher to help you with handoffs/transitions, if need be. The "Kissing Hand" (by Audrey Penn) book is a great little ritual of bonding before separating, and the book introduces this well. Your child's teacher may also be able to give you some positive pointers.