I would go back to establishing free, forward movement on the lungeline. I'm not sure what tack you use (surcingle, side reins, etc), but I just use a rope halter and 15 foot line. I have a cue stick for reinforcing my hand cues. While it's important to have contact, correctness of frame and carriage, etc. on the horse, at this point (without having seen the horse in action
) she needs to almost establish a canter uninhibited before any additional tools are added, IMHO. I think of it as, if she can't carry just herself as she's naturally comfortable at the canter, she can't do it correctly with leather hanging all over her. You need a "raw, unpasturized" gait before it can be refined. Again, my humblest of opinions, I know it will probably be criticized. When she canters calmly without bucking, accepting the gait itself, comes the refinement. I'm not familiar with the training system, but all that it does can be done with a little more time by a rider. However, in your situation, unable to ride often, it may be an option to keep your horse progressing. Unless she's cantering calmly and willingly, that contraption is a recipe for disaster if she starts bucking.
Stand just behind her driveline (about the girthline, a little ahead is better) to make sure that all pressure is directed to move her forward. Pressure, even your presence, ahead of the driveline will ALWAYS cause the horse to stop or turn, whick you don't want. Hold the line in the hand closest to the horse's head, and the cue stick (a whip can work in a pinch) held in the other hand, neutral. Send your horse out onto the circle by pointing up and forward with your line hand. If she doesn't respond, raise the stick and slowly swing it, suggesting that she move. If she still doesn't, tap her on the rump. Keep tapping until she walks. Get her well warmed up in both directions, then ask for a canter. Same cue as for the walk (raise lead hand, point ahead, encourage with the stick). I add a smooching noise to help my horse differentiate between a canter and a faster trot. At first, just get a canter, to be sure that she understands what you want. Don't worry about the demon trot. Usually, a faster response comes naturally, but if it doesn't, every time she just demon trots, slow her down (relax your body, a verbal "easy, easy") in the gait you are starting from, then ask again. Lots of transitions on the lunge. All you're doing is getting her feet unstuck, getting her willing to move forward off of a mild cue with a "Jump? How High?" attitude. It's probably best to establish this at the walk and trot first, to make it easier for her to understand at the faster speed.
That got really long, sorry, but I hope it makes sense and helps you out a bit. Good luck!