dongles, while it is true that courts weren't keen on shared residency orders, this is (slowly) changing. Particularly as a shared residency order doesn't necessarily imply a 50:50 split. Most importantly, a court will be looking to see if the current arrangement is working for DD or not - there's nothing that lyneham has said that I've seen that raises any serious concerns on that score. The problem is that this arrangement isn't working for lyneham, not her DD.
lyneham, the usual progression of negotiation for this kind of thing is a) informal between yourselves, b) via mediation, c) via solicitors, then d) in court. You could ask your ex to re-enter mediation, and/or you can represent yourself in court to reduce costs.
I'm no expert and any family court case is a lottery but I'd have to say that if you presented in court the story you've presented here, I'd not be hugely surprised if your ex is awarded sole residency. He seems to be doing everything that a court would want to see him doing - he negotiated in good faith with you via mediation and he's sticking to what he agreed to. He's got a family at his home that DD seems (generally) happy being a part of. He's stayed near DD's school. And he's not trying to make DD's contact with you any more difficult or trying to reduce it.
You, on the other hand, agreed something in mediation that you're now saying you didn't really agree with and you're now trying to change by the back-door. You're moving away from DD's school through your own choice and your own reasons, but with few benefits for DD. And you're trying to reduce the contact that DD has with her father and make what contact he does has more difficult.
In essence, the courts look at which parent is operating with the DC's best interests in mind. One of the interests they look at can be summed up as "not making things even more difficult than they already are without a damn good reason". Courts also have a default position of not changing things without good reason.
Again, I'm not expert but I reckon you'd be lucky to walk out of a court with the current, mutually-agreed shared residency arrangement re-worked as a court order. Worst-case for you is that your ex could get sole residency and you could be regarded as someone who is not operating in the best interests of your child.