most speakers of modern English don't think of "spew" as a synonym for "vomit".

I cannot speak for most, but whenever I (as a native American English speaker) read that word, my mental voice is Skippy Squirrel, and it definitely has the "vomit" connotation for me; in fact, for me, every other usage of spew derives from the "vomit": a volcano spews forth lava because it's similar to the way that a human spews forth vomit, or an idiot spews forth nonsense because it's analogous to the way that a sick child spews out breakfast. If you don't have vomit as your default definition for spew, you're lucky, IMO, because it prevents some nasty mental images when people use "spew" for the other variants.