The DFDR should have throttle position - if it splits with the autothrottle on, that would be pretty good indication that a clutch was slipping, if that split persists it would similarly be a good indication that the crew wasn't addressing the problem (or, in the case of a seized throttle, was unable to address).
They're going to need the CVR to understand the why.
BTW, it would be pretty much unheard of for the memory module to come out of it's protective steel (or titanium) protective shell. I can't tell much from the photo above, but I suspect the protective shell separated from the rest of the CVR module - it's that protective shell they need to find. If it's steel, they may be able to use a magnetic anomaly indication to help locate it.