Vivitrol is the extended release form of the drug. Since the Sinclair Method is sensitive to timing, I imagine that the usual Hydrochloride form is preferable, which goes by the brand names Revia or Depade. However, it's already generic, so no need to pay for brand names!

It's prescription only, but it's not scheduled. The ease of obtaining it is likely dependent on how willing your doctor is to bend rules, or how well you can convince him or her that you are suffering from alcoholism. Even the experimental doctors want something plausible to write down however. They may be more persuaded by the mention of other applications of the drug, such as the trials on gambling addiction.

must be administered by a health professional.

Because of the possible liver damage, as far as I can tell. I think one can (relatively) safely self-administer as long as one sticks to low doses; the principle says the effect ought to be weaker, not gone.