I know the baking soda and superglue trick! It makes the glue dry fast but can leave residue. (I always use it with Zap a Gap. Not sure if others do.)
I agree that researching glues that bond your type of plastic is the best idea! Loctite makes a vinyl glue I think. Some glues even melt the plastic a little to create a very strong bond! I recommend going to artstuf.com and phoning the people there to ask for a reccomend product, they're very knowledgable and will ship you things.