Q: How can I add a .mov video file to the beginning of an existing .mp4 video file?

I normally use final cut for all of my editing but Im having a lot of trouble converting this mp4 with bad pixelation.
The mp4 is my only master copy of my original 8mm student film.

It has some bad opening titles I need to alter and I need to slap my production logo on the front before I can even think of releasing this again.
Any ideas?