Broadcast safe doesn't mean lack of contrast. It just constraints the limits in wich a good balance can of course be acheived. I think that you should grade using the scope always.
Depending on the export, you can expand (RGB) those limits to be "correctly viewed" on computers but if you work from a broadcast safe base, you'd have no bad surprise and the shift is minimum.
But IMO you shouldn't compare that much what works for stills and what works in motion. For ex, sharpness in motion is not as relevant as for stills and could even ruined totally the viewing experience. What would be considered as harsh contrast in still might help the story in motion. Avoid thinking the same way.
Let's say you have a haunted castle in a drama. In still you would try to get texture infos, sharpness but in motion you have the clouds moving, maybe a thunderstorm and some visual effects. The eyes won't notice details the same way, there are much more infos to process, sound etc...frames are moving so the possibility to apply more extreme gradings and erase detail info can even help to tell the story, it just depends. There are also movies with extremely wide DR and no crushing B or W but because it also fits the story. Here is one with great DR and no crushings, you'll notice that there are no blacks or whites: http://vimeo.com/23903637
it's on purpose. (ARRI look)
Try to capture the max DR possible in the footage so you have room but think climate, story etc...moving images aren't made to be viewed the same way, it's a different experience.