Since you're a year out, studying from the prep books won't do you much good. Your content review would be too dilute to be of any real use. Right now I'd focus on reading various journals, newspapers, and magazines; in other words, verbal prep. After you're done with an article, analyze it. Write down the main point of the article, the author's feelings on the subject, and try to come up with some questions & answers. Think up both the right and wrong answer choices and try to imagine how the author would try to trick you into picking a wrong choice.
About the SAT and MCAT verbal, don't worry about your SAT verbal. This is this, that is that.
I don't think getting a private tutor for verbal alone (or primarily for verbal) is worth your time. There's nothing you can really learn from a private tutor that will help you on verbal outside of test taking techniques and possibly post game analysis. However, I think it's better for you to do the analysis yourself. It's easy when someone points out the thought process, but I think it's best for you to find your own method. You can find numerous verbal help threads in the MCAT FAQ that will do just fine.
Yeah I would reiterate this, there really is not a strong correlation.
SN2ED's advice is good. I'd say 6-8 months before the test is ideal to start some light review but a year is fine too I think. it never hurts, but if you do a year in advance be sure to review that earlier material again.
Before doing verbal practice passages, I think reading the Economist or NYT is a great idea just to get used to reading passages - just analyze them (don't just casually read them) using the tips sn2ed posted above. Also try to save some of the verbal until closer to date- there is less "good" verbal practice material than the sciences.
And I do not think a prep class will specifically help verbal.