When you say 'convert the edited footage,' I'm reading that as you have already edited it, but are currently saving in some other format, but not x.264.
What format is your 'edited footage' in at the moment?
Or do you mean that you need something to both edit the raw footage, and then convert it to x.264, in an MKV wrapper?
I store all my AVCHD edited footage as x.264, or Xvid, in an MKV wrapper, and I do that by converting to 'Canopus HQ', and then importing that into 'Virtualdub'.
Output from there as x.264, and put it into an MKV format using 'mkvmergeGUI'
There is a free Canopus AVCHD2HQ application from the Grass Valley website, but you'll need the Canopus HQ codec for it to work. It's not difficult to find a freeware version of that codec, but there is some discussion on the web as to whether it's supposed to be out there as freeware. You'd have to make your own mind up on that one!
Virtualdub is free anyway, but can take a bit of learning. You can Google for tutorials if you need to.
'mkvmergeGUI' is also free.
There maybe other ways, using some of the NLE's out there --maybe someone can suggest an easier way?
It's unlikey to be a cheaper way though!