It is a mistake to use nose bands to try and correct a lack of lateral flextion, just as it is a mistake to use tiedowns to correct a lack of vertical flextion.
The correct answer is what you have already been told, get back on the ground and work on lateral flextion, Obtaining vertical flextion is nearly impossible, until you have lateral flextion. Also teach you horse to disengage it's hindquarters,
Then teach it to yeild it's hindquarters to pressure, moving away from pressure. (Apply pressure just in front of it's flanks with your knuckle or thumb, when the horse takes one step away from the pressure with his hind legs, release the pressure by removing your thumb from him. Do this again and again until your horse moves instantly away from the pressure,) You will be surprised how well this works when you are on his back and you move your leg back and he moves those hindquarters around cutting his turning radius in half.
When a horse does not turn well, it means that he is not bending at the ribs, (he is stiff like a board,) this means he needs ground work to teach him how to become soft and supple.
I am not against using aids like tie downs, nose bands, etc. I just believe they should not be used to cover up improper or a lack of training. If they are used to try and hide improper or a lack of training, it is only a matter of time before the problem gets worse.
Many a horse has flipped over backwards because of nosebands and tie downs that were used to cover a lack of training.
In regards to ground work, many people are not comfortable on the ground working thier horses. But I have found the relationship between a person and a horse first begins on the ground. If you want to improve your relationship with your horse, improve your horses repsonsiveness to you. Spend some time playing with him on the ground, make training fun for you and your horse by changing up your ground training. Introduce new challenges, like jumping over objects, troting over tarps etc. then help him to successfully meet those challenges, increasing his confidence in himself and in you. You will be amazed at your horses saddle improvement and how well your horse rides.