Can you slurp words into "" somehow? I often end up with things looking like this: (str "Hello " "|" some-expression) when I'm editing text.

I don't think vim-sexp supports that. I usually just end up using x to delete the closing " and p to put it back. It's a little bit annoying.

you could construct that command using di" as a building block I bet

cursor inside "foo" - di" gets you foo in the yank buffer and a "" left in the document