Backups For Very Large, Fast Growing Data

Hi folks,

I'm a biit in a tight spot here and single brain can't work this out, maybe multi-brain can:

My situation:

1. We have a fileserver. On that fileserver our production team stores - among other stuff - their video production material. During phases of creating that, the raw material can grow quite rapidly, more than 2 TB of new data per day is not unusual. This often gets compressed later to smaller chunks with mezzanine codex that save 30%-60% space while only losing 5% of quality.
2. We have online on-premise backups and offline off-premise backup sets that total to 7 full chains, which multiplies the space used enourmously. That's slow, cheap storage, I can grow that, even tough I don't like it, but that's business.

But here comes my problem
3) A fresh full chain with compression end encyption takes at least 48 hours for the data we have, and our video-guys quickly adding 2 TB on the fly doesn't make this any faster. I resent them for it, but it's our business and I need to solve this.

- I am trying to educate them into compressing their material early and don't let all that raw data fly around on our fileserver, but when they are "in the flow" that's really not their top priority.
- I was thinking about creating a "NO-BACKUP" space for them to work with, but knowing my guys, they will f*** it up and ask for restores of "NO-BACKUP" data.

How are you guys tackling that? I don't really need polished solutions, just ideas to work with would help.

EDIT: Thank you for the quick responses, you gave me some stuff to chew on, definitely what I was hoping for.