CatBus said:

Actually stretch's suggestion to convert the audio track would allow you to keep using the MKV format, so as long as you're okay with all that demuxing, converting, and remuxing, it's doable.

Actually, when using xvid4psp it would only be demuxing and converting. You would demux with mkvmerge and then xvid4psp will do everything else in one step. You want to select Copy for copying the AVC video over. Then you select Custom for audio conversion to AAC. I'm not positive but I think you need AAC-LC selected.