Is there anyway to speed up Exchange 2007 to Exchange 2013 sp1 migration?

Have you checked the logs for the migration batch job firstly to see if there are any errors/warnings?

I don't see any errors.  I see a lot of these messages below, which might be normal.

CacheEntry setting delay interval to 00:02:00

What happens as new mail comes in during this process?

To be honest I'm not entirely sure. I know when you perform a mailbox move in Exchange 2010 to Exchange 2013 the user can still use the mailbox up until the point where the move has completed - they then get disconnected temporarily while the new Exchange server completes the mailbox move. Whether this is true for Exchange 2007 I can't be certain. Can the users who are having their mailboxes moved still work in Outlook?

There have been plenty of others who have complained about the speed of mailbox migrations when going from Exchange 2007 to Exchange 2013. If you run the Get-MoveRequest | Get-MoveRequestStatistics command in EMS, what does the StatusDetail column say for the mailboxes being moved? You can periodically run this command to check the progress of the moves. If you see no errors or warnings then unfortunately you will have to stick it out and wait for the process to complete.

Get-MoveRequest | Get-MoveRequestStatistics

This returns all queued, completed and copyingmessages statuses.  I thing I noticed is there are only 20 active mailboxes being moved. Everything else is "queued".

Is there a way to get more mailboxes syncing at once?

The only thing I see in the Event Log is Could not establish trust relationship for the SSL/TLS secure channel, but not a lot of them.

You can do it by increasing the sessions. Follow this:
http://msundis.wordpress.com/2011/01/18/increase-the-number-of-simultaneous-mailbox-moves/