I'm not sure if it would help Caro to change coaches now. It's to close to the Olympics to try something totally new and change her environment completely (I doubt that there is another world-class coach in Oberstdorf and yes, I consider Huth still as one because I think that both Caro and Tomas plus Annette all become a lot better since they started training with him and don't know something about Kovalevsky because I never followed his career closely).
Dytrt's psychologist is always on her side. She was with Annette both at Worlds and Euros, you can see her sitting next to Dytrt and Huth when they were waiting for the marks so I guess she was even with Dytrt before the skate. So I'm not sure if she still has the same psycholgist like Kostner has because I didn't see her next to Caro.
And (maybe not at Worlds but at Euros) it helped Dytrt a lot. At Euros the placed the first time under the Top 10 and she always said in interviews that both her psychologist (Huth suggested her to work with) and her new trainer helped her a lot to become mentally stronger.
As for Verner he himself said after these years Euros that his training was wrong and so he, after talking to his coaches, decided to change it. Now he trains his whole programs every day while before he just trained parts of it.
At last I don't know if there was really a heavy psychological reason for Caro's LP at Worlds or if it was just not her day that day but in all cases I don't want her to switch to Mishin! Nearly every coach else but not Mishin.
Surely there will be a lot of you who will disagree but the only feeling I have about him is that he is wasting the talent of 99% of his students. Of course he brought Plushenko to an Olympic and Yagudin to a World title and they were both great jumpers and maybe they learnt a lot about technical things from Mishin but on the artistical side he always wasted their talent (also Gachinsky who everyone thought will be the next great star - where is he now...).
I remember seeing him in a documentary dropping some choreography of Plushenko's programs because "only the technical difficulties" are important.
I prefer nice and good looking programs to ones with ten quads in it...