That problem may have stemmed from that bit being used improperly. I would ask the owners if you can start over with the snaffle to try to get him more relaxed and supple. As for correcting with one rein, even though this bit has swivel shanks, they are being held mostly stationary by the slobber bar and makes it confusing when you pick up one rein. In order for the one-rein to be effective, the shanks need to be able to swivel out to the side.
I personally don't care for bits like the one you posted because if you ever pick up the reins and contact the bit at all, there is no tongue relief and it smushes his tongue. That may be a part of the gaping problem. After you get him supple, you might also talk to the owners and see if they will let you try him in a ported bit without the roller and see if he likes it any better.