>>"I want it to work across the whole document, on any paper space. It seems when I copy the text box (referencing the text object contents) to another paper space, it loses the connection. "

I guess you "copy" it by a feature like in windows "clipboard" ?

That's the problem! (you export the data to another file and import it back to your file - this is how it works in the background)

CREATE NEW field (by pasting the field code) instead of copy&paste the (M)Text object!