I'm so glad you have decided to stick with him.
Noah obviously has problems and who better to help him through than someone who loves him and who has committed themselves to seeing it through. If you were to rehome him who is to say he would have a better home - it could be that he is unable to bond closely with anyone at this stage and he could end up being pushed from home to home without anyone actually loving him at all.
Try the tips you've been given and just let him have his own space and do his own thing as long as it doesn't break the rules

Who knows - in a few months you may be posting and telling us that he is a different dog! I hope so! But even if that is not the case at least you can be sure that he is with an owner who loves him unconditionally and wants the best for him - YOU!