Just moving the White wire is not good enough. You cannot use the Double Pole, 220V breaker. You must buy a Single Pole, 120V 30amp breaker. $7.00 or so. As for the "left side, right side". Make sure it is color to color. Meaning Black to Brass,...
DO NOT TURN IT ON while connected to 220. You will regret it. Don't try to understand electricity, just respect it and follow the rules. It is confusing and deadly. This is what you need... It sounds like you have the correct plug as you stated ...