By adding this to the .desktop file and running the following command;
sudo update-desktop-database
I've now got Media Center showing up as an option for default audio and video...
Nice! Works like a charm!
For reference, here's the full MIMEType I'm using in the .desktop file (which includes the MIME type for the .MJR license file);
MimeType=application/mjr;application/mxf;application/ogg;application/ram;application/sdp;application/smil;application/smil+xml;application/vnd.apple.mpegurl;application/vnd.ms-wpl;application/vnd.rn-realmedia;application/x-extension-m4a;application/x-extension-mp4;application/x-flac;application/x-flash-video;application/x-matroska;application/x-netshow-channel;application/x-ogg;application/x-quicktime-media-link;application/x-quicktimeplayer;application/x-shorten;application/x-smil;application/xspf+xml;audio/3gpp;audio/ac3;audio/AMR;audio/AMR-WB;audio/basic;audio/flac;audio/midi;audio/mp2;audio/mp4;audio/mpeg;audio/mpegurl;audio/ogg;audio/prs.sid;audio/vnd.rn-realaudio;audio/x-aiff;audio/x-ape;audio/x-flac;audio/x-gsm;audio/x-it;audio/x-m4a;audio/x-matroska;audio/x-mod;audio/x-mp3;audio/x-mpeg;audio/x-mpegurl;audio/x-ms-asf;audio/x-ms-asx;audio/x-ms-wax;audio/x-ms-wma;audio/x-musepack;audio/x-pn-aiff;audio/x-pn-au;audio/x-pn-realaudio;audio/x-pn-realaudio-plugin;audio/x-pn-wav;audio/x-pn-windows-acm;audio/x-realaudio;audio/x-real-audio;audio/x-s3m;audio/x-sbc;audio/x-scpls;audio/x-speex;audio/x-stm;audio/x-tta;audio/x-wav;audio/x-wavpack;audio/x-vorbis;audio/x-vorbis+ogg;audio/x-xm;image/vnd.rn-realpix;image/x-pict;misc/ultravox;text/google-video-pointer;text/x-google-video-pointer;video/3gp;video/3gpp;video/dv;video/divx;video/fli;video/flv;video/mp2t;video/mp4;video/mp4v-es;video/mpeg;video/msvideo;video/ogg;video/quicktime;video/vivo;video/vnd.divx;video/vnd.mpegurl;video/vnd.rn-realvideo;video/vnd.vivo;video/webm;video/x-anim;video/x-avi;video/x-flc;video/x-fli;video/x-flic;video/x-flv;video/x-m4v;video/x-matroska;video/x-mpeg;video/x-mpeg2;video/x-ms-asf;video/x-ms-asx;video/x-msvideo;video/x-ms-wm;video/x-ms-wmv;video/x-ms-wmx;video/x-ms-wvx;video/x-nsv;video/x-ogm+ogg;video/x-theora+ogg;video/x-totem-stream;x-content/video-dvd;x-content/video-vcd;x-content/video-svcd;x-scheme-handler/pnm;x-scheme-handler/mms;x-scheme-handler/net;x-scheme-handler/rtp;x-scheme-handler/rtmp;x-scheme-handler/rtsp;x-scheme-handler/mmsh;x-scheme-handler/uvox;x-scheme-handler/icy;x-scheme-handler/icyx;