Here's an off the wall suggestion (assuming it's available nearby), from a guy that was recently there and now has his PPL:

Send him to spin / upset recovery training. I'm not talking mushy slow, Cessna spin...I'm talking Citabria / Decathlon holy-crap-*** spin. I know it's not required for the PPL. It was required at my school. I did it, and it was amazing. It was the biggest confidence booster in the world. I wasn't nearly as bad as your student in that area, but there was lots of room for improvement. That lesson was like a switch. Being able to recognize the spin for real instead of just talking about what happens, and then recovering....it's a huge confidence boost. I felt on top of the world after that lesson and I felt I could conquer all after it (within reason of course). This confidence transferred over to all my other aspects of flying - owning the plane, not it owning you. Owning the radio calls, not clamming up. Flying LAX mini-route was an instant breeze. Crosswind landings, easy. Power on stalls, lemme show you a REAL one, mr. DPE. I literally cruised through the rest of my PPL with ease and my flying skills improved dramatically.

Seriously, only good can come from spin / upset recovery training in a plane made for it.

I highly recommend it.