That is exactly the kind of scenario I need to avoid.
As much as dedupe can be great, it sucks time out of your life when it needs troubleshooting.
A few things, and I'm sure this may have cropped up already -
Have you sealed the store recently or periodically?
Are your servers correctly speccced? Looking at that backend data size, I would say you are certainly in the "large" spec (x12 64 GB minimum)
Is your primary storage on fast disk (not cloud\object\blob etc).
Did you test your DDB volumes using iometer (correct raid group etc)
Do you have Syn-Fulls smashing the crap out of the same disks you are trying to copy from (Dash Fulls are great, but I know some people are still using Syn Fulls which destroy shared performance on plenty of shared disk libraries). If you have got Syn Fulls in play, can you either convert to Dash Full, or move to alternate storage\SP?
What SP are you on? I know there was a new version of Dedupe released in SP14 or SP15.
Disabling dedupe would not be the end of the world, but you need to identify your bottleneck.
It is quite possible that the Q&I's are red-herrings. I have managed a number of smallish clients reporting high Q&I's and we just left it, as backups and copies were easily being met.
Anyway mate - thansk for the reply, and good luck with your issues.