I haven't tried glue on foam myself, but I would suggest trying it. If it works, you can skip the newspaper/craft foam steps. if it doesn't, just glue or wrap some newspaper around your foam spikes, paint them the same color as the wig hair, and then proceed like the tutorial shows.
As far as glues go, I would highly recommend Fabri-tac!! It holds very well, is flexible, and dries clear. Tacky glue is another good one, but since it's white I feel that it doesn't dry as clear as fabri-tac does (fabritac starts off as clear). Although, Tacky glue is cheaper so it really just depends on which you'd rather buy. I've work with caulk before with wigs but to me is was more difficult to work with, and took way longer to dry.
Hope this helps, and good luck!!