CSW can request an appeal, but the appeal judge can look at the request and see if there is any actual real value evidence that can put into question the verdict, to be worth actually going to an appeal case to be seen in court..
appeals dont just happen where a request results in new court room drama, appeals can be denied if there is nothing worthy(no new compelling evidence)
especially with the forgeries, he would have to provide something really substantial, just to even get an appeal to go ahead before even getting into an appeals court
in short he has to show something compelling for it to move to a ongoing appeal case.
i feel he has drained all avenues and cant provide any real evidence worthy of an appeal
The only reason that I can think of that a judge could allow the appeal is so they can do their friend a favor and get paid more with this easy trial or as you've mentioned a new compelling evidences but at this point, I don't think that even if CSW turned the whole world upside down, scouring the earth for a new evidence to prove that he's Satoshi, I don't think that that kind of evidence would show, I guess it's really hard to admit defeat when you're a charlatan and you're so deep in your lies that even being honest isn't going to set you free.