No one has responded to this thread so hopefully the issue is not widespread, but, in case someone needs a solution: I've just written a blog post explaining the fix:

http://matt.hackinghistory.ca/2016/11/30/using-mu4e-and-org-mime-together/

Basically,

(setq mail-user-agent 'mu4e-user-agent)


plus a small change to an internal function in mu4e-compose.el


On Fri, Oct 28, 2016 at 9:29 PM, Matt Price <moptop99@gmail.com> wrote:
I've been using org-mime for a while but now that I have mu4e up and running I would like to save the outgoing mails sent but message-mode to the default mu4e sent folder (which is in a Maildir). Is there a straightforward way to do this?