Considering that the OP lives far from available instruciton in the art of lunging, and that she is just trying to get the hang of it on her own, and that she is not lunging for long periods of time, I think she is doing rather well. He horse's movement is not extraordinary, though it might be more impressive under saddle with correct encouragement.
I agree that using side reins with a surcingle and a lunge caveson is optimal. But in real life, optimal isn't always achievable right off the bat. Given her situation, she is doing well and hopefully she can incorportate as much of this good advice as possible, little by little. Her horse will not be ruined by this experimenting and learning process.