Hi Steve,
Please try Wilfred's suggestion.
Meanwhile, what did you mean when you said "I primarily use Outlook 7 on my PC"? Please describe the detailed environment of your PC, such as OS, mail client. Do you mean you use Outlook Express 7 to access your Emails? If yes, I suggest you use Outlook 2010 to access your Emails. It can sync Office 365 whenever you move or delete an Email.
Thanks,
Edward Qu