Pullum and Huddleston classify all of the above as prepositions.

Well, bully for them. I said in the beginning (or in some other thread), there's a whole lot of similarity between things called adverbs, prepositions, and verbal particles. I'll have to crack my copy of H&P's Grammar and read up to see if I agree with their analysis. In the late days of the waning of American Structuralism (right before the enfant terrible of linguistics, Noam Chomsky came along and stirred things up), folks like Zelig Harris (Chomsky's advisor at UPenn) advocated dumping all the old terminology and starting anew with semantically opaque terms like class X or class Q. Pretty much all of grammar these days has to do with the slot filling of sample phrases or sentences.

Ceci n'est pas un seing.