My annoying, uneducated and probably arrogant response is that we need to introduce a lower-touch triage process in between the prisoners and the high-touch, overloaded CS department (the courts) to reduce spurious or unmeritworthy tickets (appeals) taking up too much time and increase the time departments have available to look at the meritworthy ones.
I know it's "not as simple as that" and doubtless I'm missing a million devils hiding in the details but I wonder if there's anyone in government actually tasked with finding these suboptimal aspects of the system and if not, why not? It would surely be a huge bang for the buck.