Once again, I've answered my own question. Sorry.
So it appears that I had two mailboxes created, one called "Sent" and one called "Sent Messages".
I simply copied all the stuff out of the "Sent Messages" folder, deleted it, then in my mail client, told it to use the new folder as "Sent".
Problem solved.
I think the multiple sent boxes got created when I converted the account over to IMAP from POP.