I have never been to a tribunal where it has been rushed, the Chair of the Tribunal will explain how the proceedings will go and that they are independant from the DWP, if they believe you are repeating yourself they will tell you so.
I don't know what you mean when you say that you 'have lots of information you want to dredge up', if you are looking at past events they will not want to know, the tribunal is purely about you and your condition(s) when you were assessed.
Gary
Nothing on this board constitutes legal advice - always consult a professional about specific problems