In fact, it seems like it might be worth investing in 2 or 3 monitors anyway... screen space is cheap and might make you more productive?

Here's a small (and probably cherry-picked) collection of studies, which I haven't examined closely, but which seem to agree with my subjective impression: ~50% productivity improvement on tasks involving multiple large simultaneously-relevant windows and tight interaction loops (data analysis, in my case), less but still substantial benefit on programming.