There is a simple solution to the backlog of veteran cases
Pick a reasonable amount of time for an answer to be forthcoming say three months. If a case isn't resolved by then the veteran gets the benefits starting day one of the fourth month WITH NO OBLIGATION TO PAY THEM BACK until a decision is made. If it takes 500 plus days then the veteran gets those benefits for a bit over 400 days. Somehow I bet the government would find a way to have these cases move faster if the onus were put on them.