Once you get to “other” codecs when exporting out of Media Composer, you are at the mercy of the QuickTime engine being controlled by Apple QuickTime. Do you have QuickTime Pro on that system? Perhaps that will give you more control over the encoding parameters.
For external encoding, you would need to transcode to either DNxHD or ProRes and export QT references out and then use a third party application to encode. You will have to decide overall of that is faster and better while meeting required specifications.
Michael