Daniel Brown

I don't see a banded transition between bit-depth levels, nor do I see any "rainbowing."
 
If it were an actual banded transition between bit-depth levels, the trasition would appear sharper, and we wouldn't see all that gradation within the area in question -- there would just be more bands instead of gradation.
 
It looks like a cast shadow from the subject onto the background. The "banding" that you might perceive is probably the umbra and penumbra of the cast shadow.

It appears that you were using a large, softer and cooler source (possibly daylight balanced) and that there was warmer ambient light (possibly tungsten balanced) filling the cast shadow.

Remember you're shooting 8bit 4:2:0 - unless you are exporting 10bit - I wouldn't shoot against this uniform, neutral background, this is the worst case scenario for noise. I would go brighter, pure white even, because you can still get macroblocks as you go darker against a uniform wall like that. 

The problem is mostly chalked up to 8bit.  You really picked a really tough shot to shoot right there didn't you?   

I did say to light your backgrounds better. :P
 
I've seen this happen when the first time photographer (or seasoned photographer gets lazy, don't ask me how I know) uses only one or two lights and doesn't adequately light the background. This gives a shadow that when pushed in post gives ugh results, even in raw.

The problem is 8-bit and noise when colors are pushed and the the contrast is accentuated, which accentuates the color of noise.  If you must work with the footage, you can try noise reduction before the grade.  If your noise reduction tool lets you profile the problem areas, maybe that would be better.  You can re-add grain later if needed.  
 
If the subject doesn't move at all, you have Photoshop CC, you can run videos through Camera raw filter, put a feathered mask outside the subject, and get really heavy handed with noise reduction and 0 the saturation.
 
Best to reshoot with a stronger fill light.