On the way to DME the FO is rostered RQ because the Flight Duty Period is greater than 11 hours. So you need to Extend the FDP. The easiest way to get around not having a bunk is to change the sign on time. But that isn't going to happen.
You don't need a bunk for RQ, regional business meets the requirement. The rate is just 1/3 (max 15) instead of 1/2 (max 18). Common practice on the A330, even some of the HKG-RUH-BAH flights were 4 crew in regional business with a FDP up around 14 hours.