I'll talk in After Effects terms here, I'm not sure what compositing program you are using, but they all seem to have similar features.

In after effects consider using the levels effect to "milk" the most color range out of your 8 bit color space. Simply move the ends of the pointers so there is not flat line in the histogram on the left and right side.

On the clean footage consider adding the noise effect to the footage. This will effectivly add a "JPEG" style compression look to the fotoage. By making the clean footage a little crunchy and pumping up the saturation and levels on the dirty footage, you can find a middle ground that might make the footage changes less noticable.

I recently had to do this. I was given footage shot on digital betacam (with tracking problems) that was copied to miniDV prior to capturing. I was also given pristine 10 megapixel stills and asked to combine it all together. Once I put it together, the quality differences stuck out like a sore thumb (much more than what I detected in your video). After using the above mentioned technique, I was able to find a middle ground that gave the pieve a more balanaced look.