Padraig, you're NE - go ahead and open a support ticket so someone can help you out.
If you can revert to your 4.5.6 backup then step through 4.5.11 that might be a good idea.
He had some processes that didn't end properly coupled with a leftover zmmailboxd.pid - I believe we had to empty some redologs as well (which affects backups - so if you do so be sure to take a new full). The fact that it happened after such a big jump in upgrading was worrysome so I took a look to make sure it wasn't a bug.
I don't mind people contacting me via PM, but it's better for our collective knowledge if you use the forums & you will get faster help that way
(Or open a support ticket if you're NE & in a bind of course!)