I agree that side reins are detrimental to this kind of horse who ducks away from bit contact. I also agree that as Anabell described, you must release the front and ride so that the horse moves forward from the hind.
The rest of her description, is no doubt correct, too, but I confess would be hard for ME to do without taking up rein contact again. That is because I don't have the training in dressage , I suppose. I mean half halting and doing a lot of transitions with out the reins takes riding with the body and seat, and I know this is the correct way, but it isnt' easy.
You might also try using something without a bit for awhile. My friend's horse started to curl behind the contact and become dishonest in his forward, sucking behind the leg. She put him in a sidepull and this helped tremedously.
But to cure his fear of the bit , you do have to work in the way Anabel has described.
Lots of foward.