I broke down and emailed a doctor friend of mine and this is what he told me:
Dramamine works on the inner ear only; so if you take it once the nausea has started, it's too late. I forgot what drug he said was in it but its classified as an anti-motion sickness drug only.
Meclizine, on the other hand, is an anti-emetic as well as an anti-motion sickness drug working on the stomach AND the inner ear allowing you to take it well after the nausea has started preventing vomiting. It's also classified as an anti-histamine, which accounts for the "hangover-like" side effects. He told me if allergy pills make you drowsy, so will Meclizine, but he recommended it over Dramamine.
He recommended 1/4 to 1/2 doses taken early in the day. A brief nap will help alleviate the hangover the next morning. He also said no alcohol whatsoever while taking it.
He didn't say anything about the patch.
-Steve