I can barely read a DFDR trace, and as such I'm certainly not going to attempt to second-guess the PF's thought process, but whatever it was, the overriding theme seems to have been to keep the nose up at all costs. The reason I mention the "rocketship approach" is because I wonder if he'd got it into his head that as long as he had the nose above the horizon and TOGA set, he was safe.
While the sim was being set up, I used the time to try out various different grip techniques on the sidestick. No matter how hard I gripped or whether I was moving with the elbow or wrist I could not get more than a fractional deviation in the pitch channel when moving it stop-to-stop in the bank channel without trying to add pitch input deliberately. This is not to say it didn't happen to the PF, but I don't think it's as easy as Machinbird thinks it is.