Sand blasting on something that thick doesn't hurt anything, as long as you can keep the sand out of the inner workings. That's the problem.
I just cleaned and painted the rear on my 69. First, scrape off all the gunk. Then, power wash it. You can go to the car wash, but don't let the owner catch you! What I did after that was to go over it with stiff brushes and de-greaser, until I could hose it down and not see oil on the water. If you have rust, a solution of muratic acid will make the rust go away, just be sure to neutralize it immediately. I've also used naval jelly (phosphoric acid) but it takes a lot more elbow work, even though it doesn't rust as bad afterwards.