Hi rosie, you can send information to the Tribunals service up until about 2 weeks before your appeal date. If you manage to get it before your reconsideration has been done then send it to the DWP, it might just swing things in your favour.
I'm afraid that I don't know when the best time would be to contact somewhere like CAB.
Edit - I always send copies of my documents,unless specifically told otherwise, I don't want originals going astray! If you do send originals, make sure you have a copy for your own records. Of course, if I have something intended soley for DWP (like letters of support from friends etc), I would probably send the original of that and keep a copy for myself.
Nothing on this board constitutes legal advice - always consult a professional about specific problems