Delete Greater Than 10,000 Messages

I want to delete all messages sent from certain internal systems older than 30 days for all in the organization - about 300 mailboxes. This will total hundreds of thousands, if not millions of messages. What is the best way to facilitate this? I've played with the Search-Mailbox command with the -DeleteContent switch but it only allows up to 10,000 objects (messages) at a time.  It then indicates to use the New-MailboxSearch command but I don't see a clear-cut way to just delete the messages.  I don't want to keep them, I don't want to move them somewhere first - I just want to remove them once and for all.  Suggestions?  Thanks!  This is for Exchange 2013 CU3.