Sometimes the best thing to do is just canter, whether on the lungeline or under saddle. Let her build the muscle she needs at the canter. As she gets the muscle and strength, the slowness will come. It takes far more muscle to go slowly than fast (Counterintuitive, I know). The more she canters, the less it will have her in that "High Ho Silver!" frame of mind when she does. It will become just another gait for her. Try to collect her a bit and ride with contact, don't just let her run around all strung out, but keep her cantering. Far too many people don't canter enough (myself included, lol).
It sounds like her excess speed to the right could definitely be a lack of balance in that direction. My solution: Canter/trot 2 laps to the right for every 1 to the left to start evening her out. She probably has more canter muscle for leftward movement than rightward.
I hope that makes sense, and good luck!
A stubborn horse walks behind you, an impatient one in front of you, but a noble companion walks beside you ~ Unknown