This is such a difficult one and if you are prone to anxiety and stress, then its not necessarily a good idea to move, as moving is at the top of the stress list.
I moved from as terrible situation in London to what is supposed to be my retirement house , rural and quiet! What do I have but a harrassing neighbour with a mouth like a dirty foghorn.
Not only will moving be stressful for you but also for Charlie and its hard to jusge how much he is affected by the events around him against your stress.
All I do know is that if you have lived there 20 years you must have roots there and neighbours do move on and one cannot judge the neighbours in a new location until you have actually moved.
Do you own your house now or rent, because if you own , you would be daft to move tro renting. You have been able to cat proof your garden where you are now and change things as you want for yourself and Charlie but in a rented new place you probably would not be able to do that.
Its a very hard decision and not one to be taken lightly, I understand about anxiety cos I have suffered for years with it and maybe it would be worth speaking to your doctor and getting help for you , a bit like you have for Charlie