If I have to deal with mp4 footage, what I do to minimize some of the issues is use ReVision DeFlicker, set to “deflicker highspeed, noise reduction method 1”. It often helps in smoothing out those oversharpened edges and compression artifacts. Then add a bit of grain. Light bleed is not that much of a problem IMO, it just makes the fire look hot.
Sometimes extracting the green channel and overlaying it in luminance transfer mode helps as well. It does change the look of the footage somewhat. I doubt it does much in this case.
Kalleheikki Kannisto
Senior Graphic Designer