BDT, I wouldn't change his swing but I would help him be able to repeat his good swing.
Your on the right track, but, the stride doesn't mean there is power. I don't see him as trying to get his power from his feet. The stride is just a way for him to generate movement. I personally believe the toe tap and longer stride are a result of him constantly hearing "stay back" so he begins to stutter his momentum by the toe tap and longer stride. He is trying to be on time with his stride and movement but lacks the proper load and timing mechanisum to know how or when to start the movement.
You can stride and still use the core as the power source. I also think that if he were to load his body properly then unload it properly that he would illiminate the stutter as well. The load happens by getting the body in the proper posture and this posture is not the stance. Posture doesn't mean stance, thats just part of it. I see many bad stances, based on style and I see many different ones as well. Posture is more involved with where the hitter gets to with his body as he prepares to hit. How he coils it(load) and uncoils it(unload). Teach him proper posture and the problem will go away. Have him have just a lift-no stride and the problem will persist.