Hi ccoogan2009,
Thank you for your question.
we could follow Ronnys advice.
In addition, we suggest there is a coexist environment when we migrate Exchange 2007 to Exchange 2013. Because if there are something wrong after we migrate user to Exchange 2013, we could migrate user back to Exchange 2007, it will not affect user to use.
Message flow could go to Internet by Exchange 2013 When Exchange 2007 and Exchange 2013 are coexisted. After we migrate user to Exchange 2013 for a period without any problems, we could remove Exchange 2007 on organization.
We could refer to the following link:
https://technet.microsoft.com/en-us/library/jj898581(v=exchg.150).aspx
If there are any questions regarding this issue, please be free to let me know.
Best Regard,
Jim