Even in joining/seeking help from a Veterans Service Organization, my advice to you is to still anticipate quite a lengthy wait time!
My example: I have been deprecated from active duty since 10/06, and filed my claim shortly thereafter. My claim was partially accepted with the help of a VSO, however a portion of my claim was denied because it was stated that I did not have any documentation on a particular disability that I was claiming. This was because when on AD, and having this particular issue my medical paperwork was taken from my master record and left on site at a facility that I was sent on TDY to, in order to be tested for this particular issue. I was not actually compensated for this issue until 2008,when I happened to be in that particular city and went back to that facility to see if they, in fact had possession of my records, and they did! However, I was only compensated for my disability from the day that I submitted the missing portion of my records, and I am still awaiting an appeals board to retroactively compensate me for the time that I had initially filed my claim! All of this has been done through the VSO, and here it is 5 years later, and I'm still waiting... My point to you is, work diligently to get that which you rightfully know is yours, but don't rely on it coming to you expediently!
On a side note; I totally and outright agree with your point about the VA, I currently work for them and I see such an extreme amount of FRAUD, WASTE, & ABUSE by many who are employees, but are not veterans, and I too believe that those jobs should only be for members who served. Everyday that I go to work, it becomes more and more apparent to me that many non veteran employees DO NOT ONLY NOT CARE ABOUT AND DESPISE SERVICING OUR VETERAN POPULATION, but they are only there because of the level of security that is present within the government system! An absolute shame! Many of these employees are agents of lip service, simply but, who claim to be "here for our veterans!" Liars!