We have had exactly the same letter back from DWP, same wording but in reference to his walking, help with personal needs & preparing a meal from scratch. I wont go into his symptoms at this time but like you said it is like they are talking about a complete stranger.
I feel just as frustrated as you and we are in the process of starting an appeal.
I empathize with you. We had a four year battle to get my husband on to the right rate.
We had 2 years to get him on to dla of lower rate and then another 2 years to get his rate upgraded which happened this year at reconsideration. We had asked for a supersession and it was turned down so we put in an appeal and it was over turned before the appeal and we got my husband rates upgraded to high rate of both mobility and care. Appeal and keep on doing until you get it. We did and finally it has paid off.
You will find the template letter in the appeals part, use it and add any little bit on that you think poignant. Thats what we did and it worked.They don't like too much to read hence keep it simple and point to your Doctor letter has proof and don't give up.Good luck and let us know how it goes x