RE: What types of glues to use to repair styrofoam?
Gorilla glue expands as it dries, which helps to fill in any voids. A good thing.
I don't use it on foam because of it's color when dry.
White glue can indeed take longer to dry, but when it has the repairs are all but invisible, ( as long as there is no undue compression ).
With Gorilla glue, the glue joint appears brownish.